Transportation Economics/Print version

Transportation Economics

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Transportation_Economics

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.

About

Transportation Economics is aimed at advanced undergraduate and graduate civil engineering, planning, business, and economics students, though the material may provide a useful review for practitioners. While incorporating theory, there is a very applied bent to the course, as all the ideas covered are intended to help inform the real decisions that are made (or should be made) in practice.

This book uses two core ideas:

1. Individuals (firms, agencies, agents, actors) behave according to incentives provided by their environment.
2. The environment is shaped by the collective behavior of individuals.

The material of each page can be covered in a ninety-minute lecture.

Authors

Authors of this book include David Levinson, David Gillen, Michael Iacono, and others ...

Introduction

A toll booth on the Garden State Parkway.

Transportation systems are subject to constraints and face questions of resource allocation. The topics of supply and demand, as well as of equilibrium and disequilibrium, arise and give shape to the use and capability of the transportation system.

What is Transportation Economics?

Traditionally, transport economics has been thought of as the intersection of microeconomics and civil engineering.

Alternatively, traditional microeconomics is just a special case of transport economics, with fixed space and time, or where the good being moved is money.

Transport Economics is the study of the movement of people and goods over space and time. It is a branch of economics that deals with the allocation of resources within the transport sector. Historically, it has been thought of as the intersection of microeconomics and civil engineering, as shown on the right.

However, if we think about it, traditional microeconomics is just a special case of transport economics, with fixed space and time, and where the good being moved is money, as illustrated on the right.

Topics traditionally associated with Transport Economics include Privatization, Nationalization, Regulation, Pricing, Economic Stimulus, Financing, Funding, Expenditures, Demand, Production, and Externalities.

Demand Curve

How much would people pay for an "A" in a transportation class?

• How many people would pay $5000 for an A?
• How many people would pay $500 for an A?
• How many people would pay $50 for an A?
• How many people would pay $5 for an A?

If we draw out these numbers, with the price on the Y-axis, and the number of people willing to pay it on the X-axis, we trace out a usually nonlinear demand curve. With the exception of unusually ethical or ridiculous groups, the lower the price, the greater the number of people who are willing to pay. This rule applies to any good or service, such as the price of gasoline, which would get a similar, but not identical, curve.

Demand and Budgets in Transportation

It is often said, "Travel is a derived demand." There would be no travel without the activities being undertaken at the trip ends. Travel is seldom consumed for its own sake, except the occasional "Sunday Drive" or nature walk. On the other hand, there is always a need for people to leave home: a 20-30 minute separation between the home and workplace is common, and 60–90 minutes of travel per day total is common, even for nonworkers. We know that the more expensive something is, the lesser the quantity that will be consumed. For example, if gas prices doubled, there would be less travel. Similarly, the longer it takes to get from A to B, the less likely it is that people will go from A to B.

In short, we are dealing with a downward sloping demand curve, where the curve itself depends not only on the characteristics of the good in question, but also on its complements or substitutes.

A graph of travel demand, against costs.

The Shape of Demand

When working with demand, we need to estimate two things. First, the shape of demand (is it linear or curved, convex or concave, what function best describes it). Second, the sensitivity of demand for a particular thing (a mode, an origin destination pair, a link, a time of day) to price and time in the short run and the long run—in other words, its elasticity.

• Are the choices continuous (the number of miles driven) or discrete (car vs. bus)?
• Are we treating demand as an absolute or a probability?
• Does the probability apply to individuals (disaggregate) or the population as a whole (aggregate)?
• What is the trade-off between money and time?
• What are the effects on demand as a function of the time and money costs of competitive or complementary choices (cross elasticity)?

Supply Curve

How much would a person need to pay you to write an "A"-worthy 20 page term paper for a given transportation class?

• How many would write it for $100,000?
• How many would write it for $10,000?
• How many would write it for $1,000?
• How many would write it for $100?
• How many would write it for $10?

If we draw out these numbers for all the potential entrepreneurial people available, we trace out a supply curve. The lower the price, the lesser the number of people who are willing to supply the paper.

Supply and Demand Equilibrium

An illustration of equilibrium between supply and demand.

As with earning grades, transportation is not free; it costs both time and money. In transportation economics, costs are represented by a supply curve, which rises with the amount of travel demanded. As described above, demand (for example, the number of vehicles which want to use a facility) depends on the price: the lower the price, the higher the demand. These two curves intersect at a point of equilibrium. In the example figure, they intersect at a toll of $0.50 per km, and flow of 3000 vehicles per hour. Time is usually converted to money to simplify analysis.

Costs may be variable, and can include users' time and out-of-pockets costs. Out-of-pocket costs can be paid on a per trip or per distance basis, for example, tolls and gasoline, or fixed, for example, insurance or buying an automobile, which are only borne once in a while and are independent an individual trip's cost.

Equilibrium in a Negative Feedback System

Negative feedback loop

Supply and Demand comprise the economists' view of transportation systems. They are equilibrium systems. This means a system subject to a negative feedback process:

An increase in A causes a decrease in B. An increase in B causes an increase in A. In math terminology, A is inversely proportional to B, while B is directly proportional to A, thus indirectly causing itself to decrease.

Example: If A is Traffic Congestion and B is Traffic Demand, then increased congestion reduces demand, but increased demand increases congestion.

Disequilibrium

Many elements of the transportation system, however, do not necessarily result in equilibrium. Take the case where an increase in A causes an increase in B. An increase in B causes an increase in A. An example where an increase in A, Traffic Demand, causes an increase in B, Gas Tax Revenue, which causes an increase in Road Building, which in turn causes an increase in traffic demand. This example assumes that the gas tax generates more demand from the resultant road building than it costs in sensitivity to demand and the price, in other words, that the investment is worthwhile. This is dubbed a positive feedback system, and in some contexts a "Virtuous Circle", where the "virtue" is the value judgment (though this "virtue" may not necessarily be positive).

Similarly, there is an opposing "Vicious Circle", where a decrease in A causes a decrease in B, and a decrease in B causes a decrease in A. A classic example of this is where A is Transit Service and B is Transit Demand. Again "vicious" is a value judgment. A decrease in service results causes a decrease in the number of transit riders, and a decrease in transit riders reduces claims on transportation resources, leading to more service cutbacks.

These systems interact, for example, an increase in road building may attract transit riders to cars, while the additional drivers pay gas taxes, which generate more roads.

Positive feedback loop (virtuous circle).

Positive feedback loop (vicious circle).

One might ask whether positive feedback systems converge or diverge. The answer is that it depends on the system, and, in particular, when or where the system is observed. There might be some point where, no matter how many additional roads are built, there will be no more traffic demand, as all the drivers already consume the maximum amount of travel that can be attained. We have yet to reach that point for roads, but on the other hand, we have done so for many goods. In most parts of the United States, the price of water probably does not affect how much water used, and a lower price for tap water would not increase the rate of consumption. Substitutes (bottled water, water delivery services, rainwater collection) might be used if their prices were lower, or tap water were costlier. Price would probably affect behaviors such as lawn watering and car washing more than behaviors such as drinking.

Provision

The business of providing transportation services spans both public and private sectors.

• Roads are generally publicly owned in the United States, though the same is not true of highways in other countries. Furthermore, public ownership has not always been the norm; many countries had a long history of privately owned turnpikes, for example, in the United States private roads were common from the beginning of its history through the early 1900s.
• Railroads are generally private.
• Carriers (Airplane, Bus, Truck, and Train Operators) are often private firms.
• Formerly private urban transit operators have been taken over by local government since the 1950s in a process called municipalization. With the rise of the automobile, transit systems steadily lost passengers and money.

The situation is complicated by the idea of contracting or franchising. Often private firms operate "public transit" routes, either under a contract, a fixed price, or an agreement where the private firm collects the revenue on the route (a franchise agreement). Franchises may be subsidized if the route is losing money, or may require bidding if the route is profitable. Private provision of public transportation is common in the United Kingdom.

A London Routemaster Bus.

Principles

Specific principles of highway transportation include:

• Users commit a significant amount of their own time to the consumption of the final good. In other words, they spend time traveling. You can think of it as part of the "cost" of using the service. While the contribution of user time is found in all sectors to some extent, this fact is a dominant feature of highway travel.
• Links are routes of transportation. They are collected into large bundles which comprise a route. Individual links may be only a small share of the bundle. If we begin by assuming each link is "autonomous", then the final consumption bundle includes a large number of imperfect complements.
• Highway networks have very specialized geometries. Competition, in the form of alternative routes between the point of origin and destination, is almost always present. Nevertheless there are large degrees of spatial monopoly; each link occupies a unique space, and spatial location affects the user's contribution, time.
• There are significant congestion effects which occur both with and without pricing.
• Users choose not only a route for a trip, but whether to make that trip in the first place, to change the destination, or to delay travel on the highway network. These choices are determined by user's previous experiences. See reward systems.
• Individual links may serve multiple markets (origin-destination pairs). There are economies achieved by using the same links on routes serving different markets. This is one factor leading to a hierarchy of roads.
• Quantity cannot be controlled in the short term. Once a road is deployed, it is in the network, with its entire capacity available for use. However, roads are difficult to deploy, responses to demand are slow, and for practical purposes, deployment is irrevocable.

Thought questions

1. Should the government subsidize public transportation? Why or why not?
2. Should the government operate public transportation systems?
3. Is building roads a good idea even if it results in more travel demand?

Sample Problem

Problem (Solution)

Key Terms

• Supply
• Demand
• Negative Feedback
• Positive Feedback
• Equilibrium
• Disequilibrium
• Public Sector
• Private Sector

Games

A Game

To begin, let's play the game of Odds or Evens.

This is a classic game to determine tiebreakers or settle contests. It only requires your fingers.

1. An indefinitely repeated round-robin (i.e. play the round-robin using the schedule from the link below, and then play it again, and then play it again, and so on, until the professor says stop after some unpredictable number of repetitions).
2. A payoff matrix (see below), the payoffs are in the form of [A, B], so the first number is the payoff to player A, the second to player B. Player A is the first player in the round-robin schedule.
3. The game Odds or Evens
4. The strategy (write it down, keep it secret for now)
5. Scorekeeping (record your score … honor system)
6. The prize: The awe of your peers

Use a round-robin scheduler to determine the schedule of the tournament.

		Player B
		Odd	Even
Player A	Odd	[3, 3]	[0, 5]
	Even	[5, 0]	[1, 1]

Discussion

What does this all mean?

System Rational vs. User Rational

Tit for Tat vs. Myopic Selfishness

See Anatol Rapoport, who developed the successful Tit-for-Tat strategy for a similar, computer based strategy.

Game Theory

Game theory is concerned with general analysis of strategic interaction of economic agents whose decisions affect each other.

Problems that can be analyzed with Game Theory:

• Congestion
• Financing
• Merging
• Bus vs. Car
• …

who are the agents in each game?

Strategies

In game theory, dominance (also called strategic dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play. (ref: Dominant strategy)

Nash Equilibrium (NE): a pair of strategies is defined as a NE if A's choice is optimal given B's and B's choice is optimal given A's choice. A NE can be interpreted as a pair of expectations about each person's choice such that once one person makes their choice neither individual wants to change their behavior.

If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria. If both players have a strictly dominant strategy, the game has only one unique Nash equilibrium. However, that Nash equilibrium is not necessarily Pareto optimal, meaning that there may be non-equilibrium outcomes of the game that would be better for both players. The classic game used to illustrate this is the Prisoner's Dilemma. (ref: Dominant strategy)

		Player B
		i	j
Player A	i	[3,3]*	[2,2]
	j	[2,2]	[1,1]

Payoffs for player A are represented is the first number in a cell, the payoffs for player B are given as the second number in that cell. Thus strategy pair [i,i] implies a payoff of 3 for player A and also a payoff of 3 for player B. The NE is asterisked in the above illustrations. This represents a situation in which each firm or person is making an optimal choice given the other firm or persons choice. Here both A and B clearly prefer choice i to choice j. Thus [i,i] is a NE.

Prisoner's Dilemma

Earlier, we played both a finite one-time game and an indefinitely repeated game. The game was formulated as what is referred to as a ‘prisoner’s dilemma’.

The term prisoner’s dilemma comes from the situation where two partners in crime are both arrested and interviewed separately. If they both ‘hang tough’, they get light sentences for lack of evidence (say 1 year each). If they both crumble in interrogation and confess, they both split the time for the crime (say 10 years). But if one confesses and the other doesn’t, the one who confesses turns state’s evidence (and gets parole) and helps convict the other (who does 20 years time in prison)

In the one-time or finitely repeated Prisoners' Dilemma game, to confess (toll, defect, evens) is a dominant strategy, and when both prisoners confess (states toll, defect, evens), that is a dominant strategy equilibrium.

Applications of Game Theory to Transportation

Tolling at a Frontier

(based on Levinson, David (1999) Tolling at a Frontier: A Game Theoretic Analysis. Proceedings of the 14th International Symposium on Transportation and Traffic Theory 173-187.)

Two states (Delaware and New Jersey) are separated by a body of water. They are connected by a bridge over that body. How should they finance that bridge and the rest of their roads?

Should they toll or tax?

Let $r_{I}$ and $r_{J}$ be tolls of the two jurisdictions. Demand is a negative exponential function. (Objective is to maximize local welfare (utility of residents plus toll revenue from non-residents (toll revenue from residents is considered a transfer)).

		Jurisdiction J (New Jersey)
		i	j
Jurisdiction I (Delaware)	i	[1153, 1153]*	[2322,883]
	j	[883, 2322]	[1777,1777]

The table is read like this: Each jurisdiction chooses one of the two strategies (Toll or Tax). In effect, Jurisdiction 1 (Delaware) chooses a row and jurisdiction 2 (New Jersey) chooses a column. The two numbers in each cell tell the outcomes for the two states when the corresponding pair of strategies is chosen. The number to the left of the comma tells the payoff to the jurisdiction who chooses the rows (Delaware) while the number to the right of the column tells the payoff to the state who chooses the columns (New Jersey). Thus (reading down the first column) if they both toll, each gets $1153/hour in welfare , but if New Jersey Tolls and Delaware Taxes, New Jersey gets $2322 and Delaware only $883.

So: how to solve this game? What strategies are "rational" if both states want to maximize welfare? New Jersey might reason as follows: "Two things can happen: Delaware can toll or Delaware can keep tax. Suppose Delaware tolls. Then I get only $883 if I don't toll, $1153 if I do, so in that case it's best to toll. On the other hand, if Delaware taxes and I toll, I get $2322, and if I tax we both get $1777. Either way, it's best if I toll. Therefore, I'll toll."

But Delaware reasons similarly. Thus they both toll, and lost $624/hour. Yet, if they had acted "irrationally," and taxed, they each could have gotten $1777/hour.

Coordination Game

In Britain, Japan, Australia, and some other island nations people drive on the left side of the road; in the US and the European continent they drive on the right. But everywhere, everyone drives on the same side as everywhere else, even if that side changes from place to place.

How is this arrangement achieved?

There are two strategies: drive on the left side and drive on the right side. There are two possible outcomes: the two cars pass one another without incident or they crash. We arbitrarily assign a value of one each to passing without problems and of -10 each to a crash. Here is the payoff table:

		Mercedes
		Left	Right
Buick	Left	[1,1]	[-10,-10]
	Right	[-10,-10]	[1,1]

(Objective: Maximize payoff)

Verify that LL and RR are both Nash equilibria.

But, if we do not know which side to choose, there is some danger that we will choose LR or RL at random and crash. How can we know which side to choose? The answer is, of course, that for this coordination game we rely on social convention. Conversely, we know that in this game, social convention is very powerful and persistent, and no less so in the country where the solution is LL than in the country where it is RR.

See Driving on the left or right for historical discussion

Issues in Game Theory

• What is “rationality” ?
• What happens when the rational strategy depends on strategies of others?
• What happens if information is incomplete?
• What happens if there is uncertainty or risk?
• Under what circumstances is cooperation better than selfishness? Under what circumstances is cooperation selfish?
• How do continuing interactions differ from one-time events?
• Can morality be derived from rational selfishness?
• How does reality compare with game theory?

Thought Question

How does an infinitely or indefinitely repeated Prisoner’s Dilemma game differ from a finitely repeated or one-time game? Why?

Problem

Two airlines (United, American) each offer 1 flight from New York to Los Angeles.

Price = $/pax, Payoff = $/flight.

Each plane carries 500 passengers.

Fixed cost is $50000 per flight, total demand at $200 is 500 passengers.

At $400, total demand is 250 passengers.

Passengers choose cheapest flight.

Payoff = Revenue - Cost

Work in pairs (4 minutes):

1. Formulate the Payoff Matrix for the Game.

2. What is equilibrium ?

Solution

Solution

Zero-Sum

Zero-Sum game: If we add up the wins and losses in a game, treating losses as negatives, and we find that the sum is zero for each set of strategies chosen, then the game is a “zero-sum game."

Problem Extension

3. What happens if there is a third price $300, for which demand is 375 passengers.

Reformulate the problem.

Solution

Solution

Mixed Strategies

Mixed strategy: If a player in a game chooses among two or more strategies at random according to specific probabilities, this choice is called a "mixed strategy."

Further Applications

• Levinson, David (2005) Micro-foundations of Congestion and Pricing: A Game Theory Perspective. Transportation Research part A Volume 39, Issues 7-9 , August-November 2005, Pages 691-704.
• Levinson, David (2000) Revenue Choice on a Serial Network. Journal of Transport Economics and Policy 34,1: 69-98.

Ownership

Ownership

CosaNostra Pizza #3569 is on Vista Road just down from Kings park Mall. Vista Road used to belong to the State of California and now is called Fairlanes, Inc. Rte. CSV-5. Its main competition used to be a U.S. Highway and is now called Cruiseways, Inc. Rte. Cal-12. Farther up the Valley, the two competing highways actually cross. Once there had been bitter disputes, the intersection closed by sporadic sniper fire. Finally, a big developer bought the entire intersection and turned it into a drive-through mall. Now the roads feed into a parking system - not a lot, not a ramp, but a system – and lose their identity. Getting through the intersection involves tracing paths through the parking system, many braided filaments of direction like the Ho Chi Minh trail. CSV-5 has better throughput, but Cal-12 has better pavement. That is typical – Fairlanes roads emphasize getting you there, for Type A drivers, and Cruiseways emphasize the enjoyment, for Type B drivers. (Stephenson 1992)

The Ownership of Transportation Networks: A Rationale

To explain the patterns of public and private ownership of transportation networks in the United States and elsewhere, one would need to take a longer view of the development of transportation systems. While such explanations are beyond the scope of the current text, they may be found elsewhere. We will focus instead on some of the common economic themes that lead to observed outcomes.

Market Failure

Public ownership of transportation networks has been more prevalent in certain locations and at certain times during history. A common rationale in more modern times given in support of the public ownership of transportation facilities has been that of market failure. Though the formal concept of market failure is a relatively recent phenomenon, dating to developments in welfare economics during the early 20th century, earlier forms of it were used to justify public ownership of certain transportation facilities in the United States. In the colonial U.S., a system of post roads was maintained by the federal government (as will be discussed later), as these roads were considered vital to communication. Most mail and other types of communication moved by road, and hence it was considered critical to government administrative (and perhaps also judicial) functions that such roads be maintained. A secondary justification was that such roads would facilitate trade and interstate commerce. This is a type of positive externality argument. While it might have been possible for some such roads to be financed and built privately, there was concern that the desired network would not develop quickly enough, with lower-priority roads linking parts of the rural hinterland to established urban centers significantly lagging the completion of other segments, and thus leaving rural areas with poor lines of communication.

Other types of market failure arguments may also apply in the current context. Some road and rail networks may exhibit economies of scale, leading to more efficient provision by fewer firms with high levels of output. In an extreme case, strong economies of scale may indicate the presence of a natural monopoly, where it becomes more efficient for a single provider to produce a good. In addition to monopoly or market power justifications, there are some public good aspects of transportation networks. The next section discusses the nature of roads as different types of goods, with some local roads having the characteristics of public goods (non-rivalry and non-excludability). Private firms might undersupply a public good if there is not sufficient motivation (i.e. profit) for them to do so.

Government Failure

While the existence of market failures may provide a rationale for public ownership of transportation networks under certain circumstances, there is also a countervailing argument that cautions against public ownership as a response to instances of market failure. The public sector analogy to market failure is known as government failure, and refers to situations where government intervention causes a more inefficient allocation of resources than would occur in the absence of the intervention.

There are many types of government failure, but the ones most relevant in the context of transportation policy tend to be legislative in nature. They include issues of logrolling, pork barrel spending and rent-seeking.

Logrolling is a term applied to political allocation processes to describe the act of vote-trading among members of a political body. James Buchanan and Gordon Tullock, in their seminal work on political economy entitled The Calculus of Consent, described a formal model of simple majority voting incorporating as an example the maintenance of local roads by a group of rural farmers. Buchanan and Tullock show how bargaining (vote trading) among the participants allows for agreements that ensure the maintenance of all roads. However, the cost of this bargaining is shown to be an aggregate overinvestment of resources, since each farmer must pay for the maintenance of all other local roads in order to ensure the maintenance of the road that serves his property. There is a direct analogy between this process and the process used to allocate resources for transportation by the U.S. Congress. The rapid growth of federal transportation programs during recent re-authorization cycles, not only in terms of absolute expenditures but also in terms of the number and scope of programs, provides strong evidence of this.

Pork barrel spending has become one of the more ubiquitous forms of government failure in U.S. transportation policy. The term refers to the process of elected officials securing spending on projects or programs for the primary benefit of members of their home district. This practice has become synonymous with the process of earmarking, in which provisions are included in bills or committee reports to direct spending to specific projects, often without any form of evaluation to determine the project's social desirability. The most recent federal transportation bill, authorized in 2005, included more than 6,000 earmarks, totalling more than $24 billion in spending. The project which came to represent the most egregious example of pork barrel spending in transportation was the proposed $398 million Gravina Island Bridge in Alaska, infamously known as the "Bridge to Nowhere". Other prominent examples of pork barrel spending include Boston's Big Dig, the Johnstown Airport and Interstate 99 in Pennsylvania, and the Coconut Road Interchange in Florida. Pork barrel spending has also influenced the design of federal highway and public transit programs, both of which are structured to spread benefits as widely as possible across congressional districts in order to ensure local support.

Rent-seeking involves the manipulation of the economic environment by private individuals or groups in order to extract economic rents. Governments are a primary target of rent-seekers, since they may offer special privileges in the form of budget allocations or regulatory treatment, and are susceptible to interest group lobbying. A classic example in the field transportation is the Davis-Bacon Act, which applies to all federally-funded public works projects in the United States. The Act requires the payment of "locally prevailing" wages to workers employed on such projects. The term "prevailing" is generally understood to refer to local unionized wage rates, including fringe benefits. Originally passed in 1931, the law has survived numerous attempts to repeal it or weaken its provisions, owing largely to political support from unionized construction labor. The Davis-Bacon Act, among other provisions (such as the Buy America Act), is cited as a source of rising construction costs on many federally-funded projects.

In practice, both market failure and government failure have influenced the nature of ownership arrangements in the provision of transportation. In addition to these considerations, the type of good represented by different transportation assets may influence not only the distinction of public versus private ownership, but also which level of government should be responsible for providing transportation infrastructure and services in the case of public ownership. As we will also see, there are a range of possible outcomes in terms of the degree of private involvement in the provision of transportation.

The Nature of Transportation as a Good and Its Ownership

Elements of Vehicle/Highway System

The existing vehicle/highway system can be characterized as having a sort of quasi-private form of ownership. While in many elements are publicly owned:

• Road infrastructure
• Traffic control
• Public transit services

The system does have several elements that are privately supplied including:

• Private vehicles
• Time
• Roadside Services (Gas, Food, Lodging)
• Origins
• Destinations
• Parking

Functional Highway Classification by Type of Good

There are four types of goods that are determined by their technical characteristics concerning excludability and rivalry:

		Excludability
		Yes	No
Rivalry	Yes	Private	“Congesting”
	No	Club	Public

Public goods are non-excludable and non-rivalrous,

Private goods are both excludable and rivalrous.

Club goods (for instance a country club membership) are excludable, but non-rivalrous (in the absence of crowding).

Congesting goods are rivalrous but not excludable, for instance a crowded street. While an individual cannot be excluded from a city street, that person's presence may cost you extra time and his occupation of space does prevent you from occupying the same space at a given time. (Note that limited access highways are potentially excludable, unlike city streets.)

Excludability

Excludability implies that the good's provider can prevent a user from obtaining it without charge

National defense for instance is non-excludable, America's nuclear weapons protect anyone in the country, whether or not they want it. On the other hand, the sale of anything in a store is excludable – the owner can prevent a customer from obtaining a good unless the customer pays (assuming enforceable property rights etc.).

Rivalry

Rivalry implies that one person's consumption of a particular good prevents another individual from consuming it.

National defense again is non-rivalrous – one person's protection does not prevent another's protection. Shoes are rivalrous, only one person can wear a pair at a time.

Roads

Hierarchy of roads delineates which roads serve property access and which roads serve movement

Roads exist largely to serve two purposes: movement and access (specifically, access to property). Different types of roads have characteristics of different types of goods based on their functional classification. In other words, there is a correspondence between the functional classification of a road and the type of good it represents. What types of roads are which type of goods?

Limited access highways (freeways) and some arterials with signalized intersections and few access points, could be considered private goods, since it is possible to identify and exclude users with appropriate toll technologies. These roads are also rivalrous since, in the absence of pricing or other measures to limit demand, an additional user can affect the use of the road by others.

Local roads lie on the other end of the spectrum in terms of functional classification, since they exist primarily to provide property access. Local streets can be excludable if access to them is restricted. Access restrictions may take many forms, ranging from the simple posting of signs indicating that access is restricted to residents to actual physical restrictions, such as gates. The latter type of restriction is typically associated with gated communities or other forms of private residential development. Local streets are also generally non-rivalrous in that their low levels of traffic tend to preclude problems with congestion. This combination of characteristics (excludability and non-rivalry) indicates that some local streets may be considered club goods. The oldest such example in the United States is that of Benton Place in St. Louis, Missouri, where adjoining property owners were required to join a private association which was responsible for road maintenance, with assessments being levied on each association member.

Local streets are typically provided by local governments with no restrictions on access. In the absence of access restrictions local streets may be both non-rivalrous and non-excludable, leading them to take on more of the character of a public good. Note the term "public good" in this case is defined by the economic characteristics of the good, and not simply by the fact that it is supplied by the public sector.

Between limited-access highways and local streets are a middle level of road, collectors, that link local streets with limited-access highways. These “linking collectors” serve both access and mobility functions, since they may also provide access to some adjacent properties. These roads may be considered “congesting” or common goods.

The characterization of roads in terms of functional classification may also inform decisions about which level of government should be responsible for providing a given road (assuming the decision is made to provide the road publicly). Local units of government seem best suited to providing local streets, since they are closest to the problem. Roads that provide for a higher level of movement, such as limited-access highways, ought to be provided by higher-level jurisdictions, such as states. Of course, there are tradeoffs involved in each of these decisions. Smaller jurisdictions may not be able to fully realize scale economies, while larger jurisdictions may encounter problems with span of control. Between these extremes there is some optimal mix of expenditures between different levels of government that minimizes capital and operating costs.

Realms of Public and Private Involvement

Spectrum of transportation infrastructure ownership

One can think of the degree of public and private involvement in the provision of transportation as falling somewhere along a continuum between fully public and fully private ownership. Returning to the example of road provision, the figure outlines the various forms of possible public and private ownership structures, along with the types of functional class roads they might apply to.

Under conventional forms of government ownership and provision, responsibility for road provision is divided between federal, state, and local government. Federal and state governments have primary responsibility for arterial roads (including the Interstate system in the U.S.), with states also operating some more heavily-used collector roads. Local governments provide some combination of collector and local roads. In addition, some local roads may be provided by non-governmental organizations, such as homeowners' associations and individual private landowners (as in the case of apartment complexes).

One could also conceive of roads being provided under a public utility framework, where responsibility for maintenance and operation of the roads was transferred to a quasi-public authority. This might be an acceptable way to provide the network of linking collectors that connect local roads with higher-level arterials (limited-access highways) and serve both access and mobility functions.

Alternately, the private sector can be involved in the provision of roads to varying degrees. Most public works and transportation departments involve the private sector to at least a minimal degree in such activities as planning, design, construction and maintenance.

The more limited forms of private involvement in road provision tend to involve the outsourcing of road design, construction and maintenance activities to private consulting and construction firms. Private contractors may enter into service contracts with government agencies to provide certain specified operations and maintenance activities. These contracts may apply to all classes of publicly-owned roads. Outsourcing may also apply to more comprehensive management contracts, in which the contractor may be responsible for the design and construction of a road (often under so-called design-build project delivery systems), sometimes coupled with provisions for operations and major maintenance activities. These types of contracts often are applied to the construction of new arterial roads in cases where a public authority is unwilling to give up full control of a project.

Greater private sector involvement in terms of project financing and risk assumption are possible through agreements between public authorities and private contractors for the franchising of road projects. Franchise agreements often leave the ownership of the road in the hands of the public sector, while leasing it out to private operators who agree to operate and maintain the road for over a given period specified in the contract. This method is often adopted for projects involving the construction of new arterial roads, where the contractor is responsible for some combination of design, construction, finance, operation and maintenance activities. Many contracts are structured such that the management and operation of the road asset will revert to the public authority after the expiration of the contract. Franchise arrangements for highways also typically involve contracts that contain rather detailed provisions regarding pricing, operations, and maintenance requirements.

The greatest amount of private participation in road provision is made possible via the divestiture of existing roads by the public sector. Divestiture involves the outright sale of an existing road to a private firm, who is then free to operate the road and collect charges from users to financing its operation. Examples of full divestiture of roads are rare in the United States though, as will be discussed later, there has been some renewed interest in the franchising of existing highways in recent years.

Public Role in Private Provision of Infrastructure

The public sector has generally had three different types of roles that interact with private sector in the provision of transportation infrastructure.

• The public sector may be the recipient of privately provided infrastructure. Traditionally the public sector owns, operates, and maintains street and road infrastructure. However developers may build local roads and streets and dedicate them to the public sector as part of their role in making land suitable for occupancy. These private in-kind contributions are the most common type of private provision of infrastructure.
• The public sector may play a role as facilitator in the provision of infrastructure. Government agencies may provide planning and coordination activities in anticipation of the development of an infrastructure project, possibly including the assembly of land for right-of-way (which in some cases may require the use of eminent domain powers). Some public entities will also offer financial inducements to facilitate the provision of infrastructure. In addition to some of the tax advantages offered to private investors in the financing of infrastructure projects (which will be discussed in the next section), public entities may sometimes provide matching grants to encourage private investment. A more traditional role of the public sector in facilitating private investment has been for the state to act as a broker for infrastructure projects, combining its traditional coordination activities with the discretion to select a private developer for an infrastructure project from among multiple competing proposals.
• The third type of role that the public sector might play is to serve as an investor in infrastructure projects. Governments may serve as stockholders in some private projects, though this practice has been limited in the US (see the preceding section on the history of state involvement in US road provision for the early precedents to this policy). In some cases, the public sector may form a transportation corridor development corporation to guide the development of an infrastructure project. Lastly, the public sector may play a more traditional role as developer in an infrastructure project.

Private Role in Public Sector

There are also many situations in which the private sector plays a role in the public sector's provision of transportation. Consider the case of highways. The private sector is often intimately involved in several aspects of the development of highways. Private consultants are often hired to provide expertise in the planning and design functions on specific roadway projects. Private construction contractors are hired to manage the actual construction of transportation projects once the design work has been completed. Sometimes these functions are more closely integrated into what are termed "design-build" contracts.

The private sector may also be invited to participate in the operation of public facilities. In some cases, existing assets such as toll roads will be put out to bid for the right to operate them for a limited period of time. Recent examples of this include the Indiana Toll Road and the Chicago Skyway. Sometimes a public entity will sell an asset to a private investor, then lease it from the investor and continue to operate it, an arrangement referred to as a leaseback scheme. Under such a scheme, the public entity benefits by being able to raise cash through the sale of the asset, while the investor is able to claim the tax benefits from the depreciation of the asset.

The private sector may also be encouraged to take on a greater role in the provision of new infrastructure. Beyond the traditional planning, design and construction functions, public entities may award contracts that require private firms to take on responsibility for the financing and ongoing operation of a road. These contracts are referred to as Design-Build-Operate-Maintain (DBOM) or Build-Operate-Transfer (BOT) contracts, with the latter containing provisions for the transfer of the asset back to public ownership after a given concessionary period.

Differences in Transportation Ownership by Country

There is a great deal of diversity reflected in the international experience with the ownership and development of transportation networks. Here we will provide a brief survey of the experiences in a few of the more developed, industrialized countries of the world.

United States

Article 1, Section 8 of the United States Constitution states that:

The Congress shall have power to lay and collect taxes, duties, imposts and excises, to pay the debts and provide for the common defense and general welfare of the United States; but all duties, imposts and excises shall be uniform throughout the United States; … To establish post offices and post roads; …

Amendment IX adds:

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

Also, Amendment X provides that:

The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.

It is not entirely clear what the above provisions prescribe in terms of ownership and operation of transportation infrastructure. On one hand, Article 1, Section 8 provides for the establishment of post roads, which initially were meant to imply major routes connecting cities, essentially the equivalent of modern highways. However, as the population grew and mail service became more widespread the designation of post roads became less clear. Also, a law passed in 1838 extended the designation to all railroads. The addition of Amendment X indicates that transportation activities not under the purview of the federal government (for example, those identified in Article 1), should be left the states or to private individuals. States, in turn, could devolve some powers to local units of government.

Early federal road bills were vetoed by Presidents James Madison, James Monroe and Andrew Jackson, primarily on the grounds that they overstepped the bounds of federal authority granted by the Constitution.

One might interpret the above provisions as prescribing a rather limited federal role for transportation, especially considering the declining importance of having a set of federally-designated post roads and the development of rather robust roadway networks. In contrast, the federal role in transportation has grown considerably, particularly during the latter half of the 20th century. While states have taken on increasing roles in constructing and maintaining transportation networks, the federal government still has a large presence in terms of regulatory policy and financing. These two activities are the primary instruments through which the United States implements its transportation policies.

Currently, governments provide the majority of the system of roads and highways in the U.S. In turn, they recover part of the cost through the imposition of fuel taxes, vehicle license fees, sales taxes on motor vehicles, weight-distance charge from trucks, and various other fees and penalties (fines). The federal portion of the motor fuels tax, currently at 18.4 cents per gallon, is directed to the federal Highway Trust Fund. Most of the federal Trust Fund revenues are distributed to the states as aid for highway and bridge construction. The remaining share is distributed for mass transit grants to cities and for environmental remediation projects related to leaky underground fuel storage tanks. States add their own motor fuel taxes, which raises the US national average motor fuel tax to 47 cents per gallon. Some state and local governments also operate toll facilities, mostly roads and bridges, which account for a little over 5 percent of all transportation-related revenues. Most of the toll facilities in the U.S. are located in older, northeastern states and many of them predate the initiation of the Interstate Highway System. More recently, faster-growing Sunbelt states like California, Florida and Texas have accounted for most of the growth in the mileage of toll roads in the U.S.

The Interstate Highway System (also known as the Dwight D. Eisenhower National System of Interstate and Defense Highways) is a unique feature of the U.S. transportation system. It is comprised of a national network of over 46,000 miles of grade-separate, limited-access highways. The network was initially planned during the 1940s, while the U.S. was involved in World War II, and was presented to the public primarily as a critical component of national defense. The stated goal was to provide the ability to move large amounts of troops and equipment across the country quickly. A second important goal was to facilitate interstate commerce, coinciding with the growth of commercial truck traffic, though this goal was not as prominently promoted. Construction on the Interstate system began in 1956, under the Eisenhower administration. Today, states retain much of the responsibility for maintaining the Interstate system, with the federal government providing grants funded the federal fuel tax. The Interstate system remains publicly owned, largely on the grounds that national defense is too important to place in private hands.

Most airports in the United States are owned and operated by municipal governments or local authorities. This remains the case despite a recent attempt to privatize Chicago's Midway Airport. The privatization proposal, initiated in 2008, would have taken the form of a long-term (99-year) lease from the City of Chicago in exchange for a $2.5 billion up-front payment. The lease arrangement fell through when the consortium that would have operated the airport was unable to put together a full financing package.

The Federal Aviation Administration (FAA) imposes taxes on aviation fuels, passenger tickets and several other aviation-related items in order to fund the Airport and Airway Trust Fund (AATF). The Trust Fund, authorized in 1970 under the Airport and Airway Development Act, finances air traffic control and grants to local authorities for airport improvements. These funds are supplemented by revenues raised by local airport authorities from sources such as landing fees (based on the maximum landing weight of aircraft), passenger facility charges (PFCs), parking charges, and concessions for retail activities at major airports. Each airport has its own user charge schedules. Airport expansion costs are usually raised by airport bonds secured by signatory (major) carriers. This gives the signatory airlines power to veto any major changes to landing fee structures or airport slot allocation systems. This veto power has proven to carry weight, for example, when LaGuardia Airport's incumbent airlines blocked a recent proposal to auction off airport slots during peak traffic periods.

Airport congestion has become a recurrent problem in many locations throughout the U.S., often affecting the on-time performance of carriers. Only a handful of airports, such as those in the New York City area and Boston's Logan Airport, use landing fees during peak periods in order to mitigate congestion. The fees are typically designed to get smaller aircraft to move their flights to off-peak periods or to other nearby, less congested airports. Airport gate and Landing slots are a similar type of mechanism for allocating peak capacity. Some landing slots are transferable among carriers. However, the method used by most airports to allocate slots to carriers tends to confer windfall gains on existing carriers.

Expanding capacity at U.S. airports has proven difficult in recent years due to political and environmental considerations. When physical expansion is undertaken, it is often in the form of adding a runway to an existing airport rather than building an entirely new one. In the U.S., Denver International Airport has been the only new airport built since 1974.

Canada

Governments provide system of roads and highways;

• recovers a part of the cost through fuel taxes, vehicle license fees, and other fees and penalties;
• limited number of toll roads and bridges.

Transport Canada owns and operate most of the airports in Canada, and provide enroute air traffic control and navigational aid services;

• Toronto, Montreal's Dorval, Vancouver, Edmonton and Calgary airports were transferred to respective local authorities in 1992.
• Some examples of private provision of airport facilities;
  • Toronto airport's terminal 3 ($500 mm)
  • Renovation and reconstruction of terminals 1 and 2 ($750 mm)
• a push towards further defederalization and privatization of airports.
• recovers a part of the costs through air transport tax, landing fees, concession and other rentals, general terminal fees, parking fees, etc.

The development of Canadian policies toward transportation have some importance differences from those in the United States. Like the U.S., Canada has maintained some degree of shared responsibility for transportation between the national government and the country's 10 provinces. However, unlike the U.S., Canada has devolved responsibility to lower levels of government to a much greater degree. With the exception of air transportation and marine navigation, most transportation functions are devolved to provincial and lower levels of government. Canada has also undertaken more extensive measures to privatize certain types of infrastructure and services, particularly in air transportation (e.g. airports and air traffic control).

Canadian transportation policy, especially toward issues of ownership of transportation infrastructure, has gone through significant change since the mid-1980s, when a wave of economic liberalization affected many sectors of the Canadian economy, including transportation. The roots of regulatory reform in Canada's transportation sector can be traced back to the MacPherson Royal Commission on Transportation (1961–62), which was tasked with studying the issues of the railway industry, which came under financial stress during the 1950s when it started losing commercial traffic to competing modes such as intercity trucking and waterways. The Commission recommended broader regulatory liberalization across the transportation sector with a more limited role for government subsidy in guiding transportation policy. Many of the Commission's recommendations toward Canada's railways were adopted with the 1967 National Transportation Act, though the recommendations regarding regulatory liberalization of other modes were not. Liberalization policies toward other modes were picked up again during the 1980s under a more conservative national government.

Railway companies themselves provide their own infrastructure; roadbeds, tracks, yards and stations; Ports Canada, a crown corporation, owns and operates major ports in Canada; each port authority (e.g., Port of Vancouver) enjoys substantial autonomy.

While a department of the Canadian government, Transport Canada, has broad responsibility setting regulations and policies affecting transportation in Canada, decisions about road construction are placed under the jurisdiction of individual Canadian provinces. The Trans-Canada Highway, a transcontinental highway link, was built through a federal-provincial partnership that emphasized connecting and upgrading major inter-regional links within provinces. Apart from this effort, there is little federal involvement in the provision of roads. Roads costs are partially recovered through a combination of fuel taxes, vehicle license fees, and other fees and penalties. Fuel taxes in Canada include a combination of federal and provincial excise and sales taxes, a portion of which are directed to a Gas Tax Fund which is used to finance municipal infrastructure.

Canadian provinces make limited use of toll facilities in the road sector. The primary use of tolls on Canadian roads is to provide a revenue stream to repay bonds issued for road construction. Some highways that were initially tolled have since seen the tolls decommissioned. Most recently, the Coquihalla Highway had its toll facility decommissioned in 2008. Originally completed in 1987 at a cost of $848 million, the highway's tolls were removed after the BC government had collected a roughly equal amount of revenue during the toll road's 20 years of operation.

Private participation in the development of road infrastructure has been limited to a couple of major facilities. Ontario Provincial Highway 407 was built between the late 1980s and late 1990s under a 35-year lease to a private consortium. Under the original agreement, the highway was to be transferred back to the provincial government at the end of the lease. However, in 1999 the Ontario government passed a budget-balancing resolution that included a 99-year lease of the highway to a private consortium. The 407 facility is one of few in the world to use an all-electronic toll collection system. The other major privately developed road infrastructure project in Canada is the Confederation Bridge, an 8-mile toll bridge connecting the mainland province of New Brunswick with the island province of Prince Edward Island, off Canada's eastern coast. The Confederation Bridge was completed in 1997 under a build-operate-transfer agreement between the Canadian government and a private developer, Strait Crossing Development Incorporated. A subsidiary of the developer, Strait Crossing Bridge Limited (SCBL) will operate the bridge for 35 years and collect tolls, with the operation of the bridge reverting to the Canadian government at the end of the lease. SCBL services the debt issued to pay for the bridge's construction with a combination of toll revenue and subsidy payments from the Canadian government for the ferry services it continues to operate at a loss in order to provide transportation for pedestrians, cyclists and other types of vehicles that are prohibited from using the bridge. It is important to note that the original motivation for building the bridge was to provide a fixed link across the Northumberland Strait to better connect Prince Edward Island with mainland Canada, and to partially replace the ferry service that previously carried most traffic to the island.

Transport Canada also retains a large role in Canada's aviation system. Prior to 1996, it had responsibility for both aviation regulation and provision of air traffic services. While it retains most of its regulatory functions, Transport Canada's responsibility for provision air traffic service has been greatly reduced. The adoption of the National Airports Policy in the early 1990s led to the divestiture of many smaller airports, while Transport Canada retained ownership over the larger airports in the National Airports System. The larger airports are leased to local private operating authorities. The National Airports Policy resulted in privatization of other aspects of the aviation system as well. A new private, non-profit company (Nav Canada) owns and operates Canada's air traffic control and air navigation systems.

Japan

Japan's major intercity roads are owned and operated by regionally-based public corporations.

Regionally based public corporations own and operate major intercity roads;

• other roads financed by fuel taxes
• many toll roads make profit after paying back the capital costs of construction and expansion.

Local authorities own major airports such as Narita and Kansai International airports;

• Landing fees and passenger fees are high;
• Government subsidize construction and expansion costs

Europe

European Commission has proposed to establish a rail infrastructure company to own and maintain railroad tracks and stations, and let rail carriers use it for fees to provide competing services.

Privatization

Gomez-Ibanez and Meyer have identified three types of privatization that may apply to transportation systems. Privatization may take the form of the sale of existing state-owned businesses, private infrastructure development, or the outsourcing of conventional public sector functions by contracting with private vendors.

Sale of existing state owned business

The first type of privatization is the sale of former state-owned business (public enterprises). During the 1980s, many governments in Europe and the developing world (South America in particular) initiated the sale of state-owned enterprises. Western European countries, led by France and the United Kingdom, were eager to return to the private sector many industries that were nationalized following World War II. These industries included public utilities, transportation, and some heavy industry (e.g. British Steel in the UK). Similar developments were taking place in the developing world, led by South American countries such as Chile and Argentina. The rationale was largely the same: a belief that the private sector could operate such enterprises more efficiently. Around the same time, the collapse of the Soviet Union and the dissolution of the former Communist Bloc left many Eastern European countries to make the transition toward a market economy. This transition affected the transportation sector in a large number of countries, where governments were eager to promote private sector participation in functions such as the provision of urban and intercity bus services. Reviews of early experiences with such reforms have started to appear for countries such as Poland and Hungary.

Private Infrastructure Development

The second type of privatization involves private participation in infrastructure development. While there has been more experience outside of the United States with private transportation infrastructure development in recent years, there are some limited examples domestically. These include the privately developed SR 91 Express Lanes in California, the Dulles Greenway in the Northern Virginia suburbs of the Washington, D.C. region, and the Las Vegas Monorail, one of the few examples of privately financed passenger rail systems in the U.S. In most cases where the private sector is invited to participate in transportation infrastructure development, the primary motive is raising new money for transportation, something that can be more difficult to accomplish under a system that is reliant on tax financing.

Outsourcing of conventional public sector functions by contracting with private vendors

The third type of privatization is the outsourcing of conventional public sector functions by contracting with private vendors. This type of privatization has gained wider acceptance in the U.S. and has become fairly standard practice for many transportation and public works departments. Functions such as road maintenance and highway management are routinely contracted to private firms.

Many urban public transit agencies in the U.S. also contract with private vendors to provide maintenance services, direct operation of some transit routes, or both. For example, a number of cities in the northeastern U.S. have contracted with Amtrak or one of several private firms to operate commuter rail services. The selection of Amtrak as the operator in some cases was due to the fact that Amtrak owns the rail infrastructure on some lines where it also provides intercity passenger service.

In both cases, the primary motive for outsourcing maintenance, management or operations is financial gain on the part of government. Many governments have been able to realize cost savings in the provision and maintenance of transportation infrastructure through competitive contracting of services. The savings may then be used to either expand or improve the quality of service, to pay down existing debt levels, or to lower the burden of taxation that is borne by citizens.

Disadvantages of Privatization

Privatization of transportation infrastructure and services may also have some disadvantages. These can be categorized in terms of whether they apply to private firms or to society more broadly.

Disadvantages to private firms

• Private firms must pay taxes
• Private firms must borrow funds at market interest rates
• Private firms do not have eminent domain powers

Disadvantage to society

• Type 1 privatization (sale of state-owned businesses) may upset existing property/equity relationships. Winners and losers are created.
• Cost savings may lead to unemployment when firms cut back on unprofitable services. These workers must find employment elsewhere in the economy, something that may not easy to do during periods of recession.
• Environmental sensitivity may not be in a private firm's objective function.

Lessons for Success

Privatization is easier when:

• There is competition in input and output markets
• Possible efficiency gains are large
• Few redistributions or transfers are required
• There are few controversies with the environment or opposition to economic growth
• An activity or service covers its cost BUT profits are not TOO high

Transit Bus Privatization

One industry within the transportation sector where privatization has gained momentum in recent decades has been bus transit, particularly urban (intracity) bus services. The relatively low fixed costs associated with provision of bus services provides the potential for a market with relatively low barriers to entry and intense competition.

Regulation Cycle

Like many modes of transportation, urban bus transit has gone through many stages of growth, maturity, decline and some degree of rationalization. Gomez-Ibanez and Meyer have identified a 10-stage cycle of regulation and privatization that broadly reflects the experience with bus transit in many countries around the world. The 10 stages are listed below.

1. Entrepreneurial
2. Consolidation
3. Regulation of Fares and Franchises
4. Decline in Profits
5. Withdrawal of capital and services
6. Public takeover
7. Public subsidies
8. Declining efficiency
9. Vicious cycle of subsidy cuts, fare increases, service cuts, declining riders
10. Privatization [Go to 1 or 3]

While most cities begin at the first stage (entrepreneurial) of the cycle, some remain in the stages of public ownership and subsidy (stages 6 and 7), while others have moved on to various degrees of privatization (stage 10). Where privatization has taken place, the cycle indicates that cities typically revert to either an entrepreneurial phase or to a phase in which services are privately provided, but certain aspects of provision such as fares and franchises are regulated.

Types of Privatization

Depending on which policy objectives are being pursued, bus transit privatization may either eliminate or supplement public ownership. Where governments are looking to divest themselves of the ownership and operation of buses services and to end or limit the provision of subsidies, they may allow greater entry for private providers and limit regulatory involvement. Partial forms of privatization can also allow governments to continue to pursue certain social objectives (for example, providing service to low-income users), while maintaining ownership of bus service. An example of this is the competitive tendering of bus services, which is a more common form of partial privatization in the U.S., where the public sector retains ownership of bus services but enters into a contract with a private provider to operate the service. Decisions on fares, scheduling and service levels typically remain in the hands of the public organization.

Conditions on Privatization

Fares

• Deregulation of fares (Colombo Sri Lanka, Santiago Chile) [Colombo kept the public company with low fares and overcrowding; Santiago had a proliferation of modes, drivers formed route associations and raised fares, service is better but still crowding]
• Regulation of fares (everywhere else)

Routes

• Deregulation of routes ... direct subsidies to specific routes
• Regulation of routes ... must provide service on unprofitable routes -> cross subsidy

Britain's Buses

The most high-profile experiment with transit bus privatization in recent history has been the privatization and deregulation of local bus services in the UK. Privatization began with the passage of the Transport Act of 1985 which privatized and deregulated bus services throughout the UK, though London did not fully deregulate its services, opting instead for a system of franchised routes. The Transport Act was passed under the conservative Thatcher regime, as part of a series of sweeping economic reforms which privatized several former state-owned enterprises.

The Act requires only that firms register the commencement of, or changes to, a bus service at least 42 days in advance. Under the law, bus operators are only allowed to offer scheduled services, prohibiting jitney-type services. Local governments may refuse to allow a service only in the event of serious safety or traffic congestion problems. They may also supplement privately registered routes by offering unserved routes for competitive tender.

New entrants - low cost by lower wages, lower overhead, flexible work rules, do not usually lower prices, passengers are unlikely to wait.

The privatization and deregulation of bus services in Britain was designed to inject competition into the supply of bus services and thus to exert downward pressure on costs. This goal was largely achieved, as new entrants with with lower costs entered many markets and exerted pressure on incumbent operators. The newer firms tended to achieve lower costs through lower wages, more flexible work rules, and lower overhead costs. Existing firms were forced to respond by cutting their own costs. Since these firms retained many employees from their pre-deregulation days while simultaneously hiring new workers, a two-tiered wage structure began to emerge reflecting the compensation of these different groups. Another source of cost savings was the substitution of smaller vehicles (minibuses), operating more frequently and at higher speeds, for larger buses. Heseltine and Silcock report that just a few years after the initiation of deregulation, former National Bus Company operators claimed to have reduced costs per bus mile by 15 to 20 percent, while former Passenger Transport Executive operators reduced costs by an average of 30 percent.

While significant cost savings were achieved by the deregulated operators, passenger fares increased as broad-based government subsidies were withdrawn. Examining the experience with the first 10 years of deregulation, Mackie et al. reported that throughout the UK, passenger fares increased by an average of about 19 percent, while real subsidies declined by an average of 38 percent. Demand, measured in terms of passenger journeys, declined by an average of 22 percent nationwide, thought the decline was much lower in the London metropolitan region. Higher fares were an important factor in explaining the decline, as was the instability in the newly deregulated bus markets. However, the decline could not be accounted for by diminished service levels, as bus-kilometers of service rose in every region examined.

One of the more interesting developments in the evolution of the deregulated bus industry was the competitive strategy that was employed by the newly-private firms. There were initially many small operators in most of the larger markets, though the industry became much more concentrated within a few years, either through the exit of unprofitable firms or through acquisition of smaller operators by larger competitors. There are essentially no economies of scale in providing local bus services, but large firms have been able to successfully drive out competition by engaging in price wars and using profitable routes to subsidize fares on more competitive routes (cross-subsidization). Maintenance of competitive conditions on routes is made even more difficult by the scheduling practices employed by the deregulated operators. Since operators may set any schedule they like, subject to the provision of publishing the change six weeks in advance, many competing operators have an incentive to engage in "route jockeying" or "headrunning", wherein an operator schedules its service to run immediately ahead of its competitors (and thus take its competitors' customers). This practice works since passengers are often indifferent to which bus they choose to reach a specific destination, provided prices and quality are roughly equal, and is made easier by the fact that operators must publish their schedules. Such a strategy often invites retaliatory behavior by incumbent operators, who have been observed to respond by running service so frequently as to prevent competitors from attracting sufficient patronage to survive, a practice known as "route swamping".

In contrast, transit contracting in United States consists mostly of paratransit services, with only some fixed routes.

Curb Rights

Drawing on the experience of bus deregulation in the UK, as well as previous experience with private provision of transit the United States and around the world, Klein et al. diagnosed the problems associated with private competition in bus transit as an absence of property rights. Specifically, they suggest that fixed-route (though not necessarily fixed-schedule) transit services are able to function where operators have a right to pick up congregations of passengers along a route.

The congregation function in urban transit is considered essential to establishing a market for transit services. Klein et al. note that the establishment of private jitney services (services operating with smaller vehicles on relatively fixed routes, though not on fixed schedules) is common where there are substantial congregations of passengers at points along a route served by a regular, fixed-schedule service. Particularly in "thick" transit markets, the fixed-schedule service acts as an "anchor" around which the private jitney operators target their service. Klein et al. draw on a historical example from the US of jitney operations emerging during the 1910s and picking up passengers along the routes of streetcars, often running ahead of the scheduled streetcar arrivals. However, problems may arise when there are no rights assigned to pick up passengers at particular locations and during particular time periods. In the case of the streetcars, the issue was dealt with by the streetcar operators appealing to local governments to enforce their exclusive franchise rights and drive out the jitneys. While this action may have (temporarily) preserved the streetcars' viability, it also drove out potential market entrants who were willing to provide valued services to customers.

In the case of thick markets, like the streetcar example, the problem of "interloping" (or inter-temporal poaching of passengers) by new market entrants like the jitney operators is not as severe. If demand levels are sufficiently high, a route can sustain several competing operators. However, when markets are "thin" (i.e. when demand levels are lower), the problem of interloping becomes more severe. When a number of competing operators enter a thin market where scheduled service is provided, the anchor of the scheduled service may be "dissolved" by the competing operators. Operators may be hesitant to invest in providing scheduled service if they cannot appropriate the returns from picking up congregations of passengers and are not protected from interloping competitors. If interloping continues to occur in this kind of market, the result may be the destruction of the market altogether. This process has been observed in many of the smaller cities in the UK following deregulation, where intense competition and frequent interloping have become destructive and resulted in a large amount of concentration among a limited number of operators.

One possible solution to this problem that has been used in the past has been for a local government to offer exclusive rights to operate a particular route. However, this type of arrangement creates many of the same problems typically associated with monopolies (higher prices, lack of innovation in service provision). The role envisioned by Klein et al. for government is one of creating and enforcing property rights to serve passengers at particular locations and times ("curb rights"). The term "curb right" is used to denote the fact that the operator would have rights over a particular space along a street (a "curb zone"), including a bus stop area and the adjoining sidewalk, which would serve as a location for passengers to congregate. These curb spaces could then be auctioned to private operators who wished to use them to pick up congregations of passengers. The provision of rights over these congregations of passengers would ensure a minimal market to establish regular, scheduled service and protect this market from interlopers. Klein et al. also suggest the possibility of local governments protecting against monopoly abuse by reserving some curb zones as "commons" areas for jitney services when a single firm seeks to buy up all of the curb zones along a particular route, giving it a de facto monopoly. Where markets are sufficiently thick, the establishment of curb rights can also improve the quality of services by ensuring a market for both scheduled services and unscheduled, jitney operations.

Road Privatization

Unlike buses, roads are not easily contestable. Buses tend to have low fixed costs and higher variable costs, which implies few barriers to entry. The roads most likely to be private (limited-access roads) under the framework discussed previously also tend to be more costly to provide and entail high fixed costs. In this case, market power is a serious consideration. Many limited-access highways function essentially as local monopolies, making the introduction of direct competition difficult.

Issues of competition can also be problematic in urban settings. Where new private toll roads or road capacity are built in urban areas, the toll road must often compete with one or more free alternatives, making it difficult to attract sufficient traffic. In the case of the privately built 91 Express Lanes in Orange County, CA, the local topography made the provision of parallel routes difficult. The primary competitor to the toll lanes was the parallel free lanes on the SR-91 freeway, which tend to become badly congested during the peak period. After several years of operation, the worsening peak-period conditions on the free lanes led to growing public demands for additional capacity. While the significant peak-period congestion ensured a market for the toll road, it also imposed a heavy economic cost on the users of the free lanes in the form of delays. Since the lease agreement with the private operator prohibited the addition of untolled capacity, the Orange County Transportation Authority had no choice but to purchase the toll road and take over its operation.

Other aspects of road networks can also make privatization difficult. For example, on low volume roads, tolls often cannot recover costs. This typically leads to other forms of financing. One possibility is to finance such roads through general revenue sources, essentially treating them as local public goods. Another is to adopt shadow tolls or other forms of availability payments.

Roads are also a long term investment, implying a need for guarantees of stability. Long-term traffic forecasting is difficult and often involves large margins of error. Uncertainty about future traffic demand translates into uncertainty regarding future revenue streams from road tolls. Under private financing arrangements, risks associated with revenue uncertainty often get capitalized into interest rates, leading to higher borrowing costs. Problems of uncertain traffic demand can be particularly acute when a private road is being built in a growing area, where future development is anticipated to form a significant part of the base of demand for the road. An illustration of this problem is provided by the experience of the Dulles Greenway in Loudoun County, Virginia, where the Greenway's original owners defaulted on their loan due to lower-than-projected demand and revenue.

Reluctance

Since the establishment of the publicly-owned National Highway System in the U.S. there has been continued reluctance to build new private roads or privatize existing roads. There have been a handful of exceptions, however. During the 1990s there were two notable projects that involved private ownership and financing: California's SR91 Express Lanes and The Dulles Greenway). More recently, the privately financed and developed South Bay Expressway was completed in 2007 in the eastern suburbs of the San Diego region. In addition, there have been a couple of cases where existing toll roads have been leased to private entities under long-term lease agreements (an example of the "franchise" framework discussed previously). These types of arrangements have been agreed to for operation of the Chicago Skyway and the Indiana Toll Road.

There are several possible explanations for the reluctance to move toward greater privatization of roads in the U.S.:

• The reluctance may reflect apprehension toward privatization in general, due to some high-profile and problematic experiences with privatization and deregulation in other industries such as California's electricity deregulation and Britain's experience with Railtrack.
• Private roads must offer a significant and apparent advantage over public control.
• The burden of proof is on those who want to change the status quo. They must prove why privatization would be beneficial to all interested parties.
• The case for privatization must be compelling, and for most places to try it, it must have been done somewhere else first.
• Not just net gains, but also distributional effects must be considered. Privatization may create winners and losers, and the losers are likely to be the most vocal opponents, complicating matters politically.

Thought Question

The 2000 Libertarian Party Platform asserts "Government interference in transportation is characterized by monopolistic restriction, corruption and gross inefficiency. We therefore call for the dissolution of all government agencies concerned with transportation, … We call for the privatization of …, public roads, and the national highway system. …"

Is Government Ownership Characterized By:

• Monopolistic Restriction
• Corruption
• Gross Inefficiency

Would Private Ownership Be Characterized by:

• Monopolies
• Corruption
• Gross Inefficiency ?

Public Policy Questions

Should the freight railways continue to provide their own infrastructure ? If yes, should they be subsidized to the extent that truckers are being subsidized indirectly ?

What are the advantanges and disadvantages of creating a common rail infrastructure corporation ?

Should the governments (i.e., tax payers) subsidize a part of infrastructure costs ?

Should the extent of subsidy be equalized across all modes of transportation ?

If so, should we subsidize an equal amount per passenger-km or an equal proportion of the total modal costs ?

Exercise

Who should own Metro Transit? How should it be organized? Work in pairs, identify alternative ownership regimes, discuss their merits.

Regulation

Regulation

Objectives for Government Intervention

There are many different objectives that governments might pursue by way of intervention in private markets. These objectives fall under a few broad categories that characterize many of the efforts at government regulation. The following are some of the more commonly observed regulatory objectives.

Maximize social welfare

Among the most common set of objectives for government regulatory policy is the maximization of social welfare through the remediation of various types of market failure. For example, agents can gain market power through the creation of monopolies, cartels, or other forms of organization that limit the benefits from competitive markets and trade. Natural monopolies are one such type of market failure that has been prevalent throughout the historical development of transportation networks, often due to the high fixed costs of developing infrastructure.

Externalities are another common type of market failure that can justify regulatory intervention. Regulatory efforts toward externalities often focus on negative externalities. For example, in the context of transportation many modes experience congestion where prices as a means of rationing capacity are absent. Likewise, the consumption of energy often leads to emission of pollutants which, when unpriced, can lead to undesirable outcomes. Positive types of externalities are also possible and can in some situations justify government intervention. For example, in systems where Network effects are present, government may be able to increase social welfare by speeding up the growth of the network so that it serves a large number of users.

Other types of market failure justifications for intervention involve the provision of certain public goods (a classic example being national defense) and the remediation of some types of information asymmetry.

Macro-economic objectives

A second set of objectives that are pursued primarily by national governments revolve around macroeconomic performance. Macroeconomic objectives include efforts to control inflation, for example through the adoption of monetary policy. They also include efforts to counteract the effects of economic cycles, for example by adopting policies to maintain employment during periods of recession. Some governments may also seek to actively control their country's balance of payments through the use of policies aimed at promoting or discouraging exports or imports (e.g. through tariffs and subsidies).

Socio-economic objectives

Government may also intervene in order to promote a range of socio-economic objectives. Many of these objectives may be motivated by concerns over fairness, such as efforts to achieve a desired income distribution, or a desire to provide a basic standard of service to all citizens, such as programs that offer mobility to people with mental or physical disabilities. Other interventions may be designed to promote safety where it is thought that market participants are unable to account for certain types of risk. An example of this in the United States is the Consumer Product Safety Commission (CPSC), an agency that has the authority to regulate the sale and manufacture of thousands of consumer products. Still other socio-economic objectives may include things like industrial policy, where governments intervene to promote certain sectors of the economy, or even to promote individual industries or firms.

Other objectives

Apart from the three categories of objectives for intervention listed above, governments may intervene for other reasons broadly related to national interests. Some interventions are undertaken to promote national unity, such as the construction of the Transcontinental Railroad in the US during the Civil War. The provision of national defense which, as noted above is an important type of public good, is almost universally seen as grounds for government intervention. Finally, some interventions are undertaken in order to promote national prestige. Efforts in many world cities and their respective countries to attract the summer or winter Olympic Games, which may often involve the development of expensive new infrastructure projects, might fall into this category.

Instruments of Government Intervention

Governments have many different instruments of intervention at their disposal in order to pursue the types of objectives outlined in the previous section. These may range in scope from simple instruments such as exhortation and information provision to actual ownership and operation of enterprises in certain industries. Regulation is among these instruments and will be introduced in the context of some of the more common instruments of intervention.

Moral suasion

Here, government attempts to affect user choice through propaganda.

• speeches, conferences, information,
• advisory and consulting bodies,
• studies/research
• reorganizing agencies

Governments and politicians may influence policy outcomes in ways that involve little or no direct expenditure or regulatory action. The provision of information by itself may sometimes be enough to influence desired outcomes. Public speeches and exhortation may sometimes be used as a way to influence support for a particular policy. For example, the US Vice President Joe Biden, a former senator from the state of Delaware, frequently commutes to Washington, D.C. by rail on Amtrak, the national passenger rail service. He often uses public speaking engagements to tout the benefits of Amtrak and to encourage support, both through actual patronage of the system and through support for additional public spending.

The use of exhortation to influence policy outcomes is one example of a set of policy instruments collectively referred to as moral suasion. Moral suasion strategies may rely on a variety of mechanisms in order to enhance policy success, but they tend to have common elements of the use of persuasion (such as appealing to moral authority or community spirit), as opposed to outright coercion, in order to achieve desired outcomes.

Several prominent examples of the use moral suasion appeared in the US during World War II. The US government used several types of propaganda appealing to citizens' sense of patriotism in order to mobilize resources for the war effort. Posters were issued by the government and distributed throughout the country to promote programs such as the planting of victory gardens and investment in war bonds. The propaganda poster to the right, promoted the conservation of energy through voluntary carpooling (referred to in the poster as "car-sharing") during WWII, appealing to citizens with the phrase "When you ride alone, you ride with Hitler!".

In addition to exhortation, several other types of instruments of moral suasion are frequently used. These include the promotion of research, organization of academic or professional conferences on a given topic, the establishment of advisory and consulting bodies, and the reorganization of existing agencies. Where regulatory bodies are involved, the threat of regulation (if not actual use) can sometimes be used in order to achieve compliance. While moral suasion in general does not serve as a good substitute for more direct economic incentives, it can complement other types of policy instruments in order to increase the chances of policy success. Romans identifies two necessary conditions for the success of a moral suasion policy:

1. The public must support the government's position
2. The populations to be persuaded must be small

Recent successful efforts to promote recycling and discourage smoking include large elements of moral suasion.

Government expenditures

One of the more common methods of government intervention is to provide direct expenditures in order to ensure the production of goods considered socially beneficial. Government expenditures may be justified on the grounds that they promote the provision of public goods or quasi-private goods that have some public good aspects, such as education. Grants and subsidies may be used to encourage the production of a good by public or private sector. Often these instruments are combined with the direct public provision of facilities. For example, the US federal government makes grants to state and local governments for the provision of highway and public transit networks, payed for largely with revenues from the Highway Trust Fund. In most cases, the recipients of these funds are public entities that build and maintain these networks. A common rationale for the public provision of these networks is that they display characteristics of natural monopolies.

Regulation - economic and other regulation;

Governments may also reserve the right to regulate certain activities for economic, social or other purposes. In the transportation sector, for example, many industries have market structures that inherently limit entry and can lead to concentration or monopoly (e.g. railroads, airlines). Rather than provide these services directly, many governments have chosen instead to maintain private provision, subject to some form of regulation. Some examples of these will be provided in the next section. In the US, the power to regulate transportation derives mostly from the Commerce Clause of the US Constitution.

There are many instruments that governments may use in order to implement and enforce regulation. Most government regulatory bodies promulgate rules or guidelines in order to set standards of firm behavior in a regulated industry. Fines and penalties may be used as tools of compliance in order to punish violations of established rules. In the context of international trade, where sovereign nations may have no formal legal powers over their trading partners, taxes and tariffs may be used in order to influence trade activities. These instruments may also be used by voluntary associations that govern trade activities, such as the European Union and the World Trade Organization.

Government ownership and/or control of enterprise

Where other forms of regulation are deemed infeasible for dealing with potential market failure problems, governments may simply choose to directly provide a good or service through a public agency or state-owned enterprise (sometimes referred to as a crown corporation). The use of public ownership may allow governments to set more efficient prices in cases where production is subject to strong scale economies, or where regulation of an activity through conventional means is particularly difficult. Government provision of a good may rely on direct ownership and operation, or may involve some form of private involvement, perhaps through a lease arrangement with the public owner. This type of arrangement will be discussed further in the chapter on ownership.

Rationales for Economic Regulation

Economic regulation is an attempt by government to deliberately alter the allocation of resources and distribution of incomes away from that which would have occurred in the absence of such regulation. It is thus a means by which government can attempt to substitute its judgement of what constitutes a 'proper' allocation of resources and distribution of income for the outcome yielded by the market. Transportation had been a heavily regulated industry in the US until recently.

There are two major opposing theories on why economic regulations exist, consumer protection and industry protection, which are discussed below. Some other rationales for regulation are also described which don't fit neatly into these two categories.

Consumer Protection

The traditional and ideal view is that regulation is a device for protecting the public against the adverse effects of monopoly. This view, as described by Posner, is commonly referred to as the public interest theory of regulation. Nominally, the main objective is to maximize social welfare by correcting market failure, which may occur in several forms.

For example, governments may choose to regulate monopolies in order to force them to produce the level of output that maximizes social welfare. Monopolies may arise for a couple of reasons. In some cases, an industry might be inherently "monopolistic" due to the existence of economies of scale, limited markets, or requirements for high levels of initial investment, which may deter entrants. In other cases, industries may exhibit high fixed costs (indvisibilities), common and/or joint costs, which make them prone to monopoly.

Another consumer protection rationale for the provision of regulation is the need to correct for externalities. Where negative externalities like pollution are present and serious enough to merit intervention, governments may intervene to correct these externalities by regulating the quantity of pollution emitted, or by setting higher prices to induce less production/consumption of the externality.

Industry Protection

The contrasting and more recent view, that of regulatory capture, is that regulation is procured by politically effective groups (assumed to be composed of the members of the regulated industry itself), for their own protection.

The reasoning behind this view is that industry attempts to acquire regulation mainly because regulation will help them generate economic rents. Furthermore, producers in an industry are more likely to have an incentive to influence regulatory activities, given their greater financial interest relative to individual consumers. Thus, producers are far more effective in pressuring government than are general interest consumer groups. Stigler argues that producers essentially "capture" regulatory agencies, stating that "as a rule, regulation is acquired by the industry and is designed and operated for the industry and not for the "public interest" (p. 3). Therefore, regulatory commissions end up "protecting" industry from consumers, conferring benefits on producers that they would not be able to obtain in more competitive markets. Stigler's ideas were formalized in a later paper by Peltzman.

Similar arguments have been used by political scientists to describe the relationship between Congress, federal agencies, and interest groups, often under the term iron triangle. In this case, the relationship is tripartite, disaggregating the role of government into objectives pursued by elected officials and those pursued by agencies responsible for administration and oversight of federal programs. This framework has been used to analyze the behavior of certain federal agencies, such as the Tennessee Valley Authority, as well as to describe the dynamics of industry-government relationships in the Military-industrial complex.

An interesting variation on the regulatory capture framework, commonly referred to as Bootleggers and Baptists, has been applied to describe situations in which incumbent firms demand greater regulation, often with lobbying support from groups with conventionally opposing positions . The namesake application of the theory describes the phenomenon, frequently observed in southern states, of alcohol sales being banned on Sundays. The ban is supported primarily by Baptists and other groups that seek to limit the consumption of alcohol, ostensibly for moral reasons. The ban also enjoys tacit support from illegal suppliers of alcohol (the "bootleggers"), who benefit from the prohibition in the form of greater market power in the provision of alcoholic beverages on Sundays.

Outside of this traditional application, the framework has been applied to other areas of regulatory policy, such as certain aspects of environmental regulation. The framework describes regulators' preference for certain technology-specific mandates (e.g. "scrubbers" for power plant smokestacks in the 1977 Clean Air Act) as a means of reducing pollution. In this case, environmentalists demanding greater regulation to ensure better air quality serve as the Baptists, while the equipment suppliers who manufacture the scrubbers serve as the bootleggers and lobby for specific provisions requiring the use of scrubbers.

A common feature of firm behavior in this framework is the use of regulation to obtain market power, often through entry restrictions. In the clean air example, plants that must comply with the regulation often have incentive to support it after it has been implemented. Compliance in this case involves one-off expenditures on the procurement of the pollution control equipment. The equipment might be expensive, but becomes a sunk cost after implementation. The requirements for this expensive, new equipment become a barrier to entry for prospective firms looking to enter the market. The incumbent firms also tend to operate at higher levels of output, thus enabling them to spread the costs of the pollution control equipment across a greater number of consumers, lowering average costs.

Infant Industry

Economic regulation has also historically been employed in some cases where a government sought to promote the growth of an infant industry. The infant industry argument for regulation is typically invoked in cases where a nation sees the existence of potentially large external benefits from the growth of an industry, or the potential for other important non-economic benefits. A classical example of the promotion of an infant industry is the US federal government's promotion of the growth of air travel on the grounds that it would provide a faster, cheaper and more effective means of delivering air mail. While air mail was initially provided by the US government between 1911 and 1918, the 1926 Kelly Act contained provisions that required the US Post Office Department to contract with commercial air carriers for the delivery of air mail on intercity routes. These contracts were an important source of revenue for the nascent airline industry.

The mail contracts may be considered a form of implicit subsidy to the early airline industry. In addition to subsidization, other instruments that may be used by government to promote infant industries include regulations on entry (entry barriers) or regulations mandating the supply of a specific quantity of a good.

Cut-throat Competition

Governments have sometimes intervened in markets in order to prevent what is know as destructive or cut-throat competition. Cut-throat competition is one example of anti-competitive business practices, that is, practices that reduce or prevent competition in a market, and is characterized by competitive situations where prices do not cover production costs over extended periods. Several types of outcomes may emerge from such competitive environments which could provide a theoretical justification for some form of regulatory intervention:

• instability in supply prices -- governments may regulate to smooth out output prices
• uneconomic rate levels;
• predatory pricing, where firms set artificially low prices in order to deter competition from potential market entrants, or to drive existing competitors out of business.
• immature pricing behavior -- oligopolists may overreact to a competitive event, as when airlines engage in price wars
• high fixed cost with slow adjustment - short run pricing falls below average total costs, especially in recession when there are a lot of excess capacity

When dealing with instability in supply prices in certain industries, as for example with electric power, regulation is used to smooth output prices. In other cases, as with road networks, the infrastructure tends more often to be publicly owned. In the case of road networks, especially in urban areas, congestion can create instability in supply prices, since the "supply" function for a road link is a function of traffic volumes. To achieve efficiency in this case, governments (or even private owners) can set prices equal to marginal cost in order to eliminate the congestion externality and smooth output prices.

Uneconomic rate levels can arise (at least in the short run) through anti-competitive practices, though in practice it has more commonly been the result of regulatory rate-setting practices that have been ameliorated through regulatory reforms. For example, many streetcar and subway networks in the US were formerly privately owned, though as participants in local franchise agreements with local governments they were subject to several forms of regulation, including price regulation. Limits on the rail operators' ability to increase revenues through fare increases, which were politically unpopular, were a contributing factor toward the decline of many urban rail systems. The inability to raise revenues through fares frequently led to deferred maintenance of the capital stock of these systems, which in turn led to declining service quality and lower ridership, an example of a vicious circle.

Predatory pricing is most common in markets characterized by few firms, intense competition and low profit margins. Deregulated local bus services in many British cities have seen instances of predatory behavior, such as the Darlington Bus War which took place in the English town of Darlington following the deregulation of local bus service in the mid-1980s. The fact that local bus services in many British cities continue to be supplied by a single, incumbent firm in spite of some limited competition from new market entrants has led some observers to suggest that urban bus services may be natural monopolies.

Immature pricing behavior has been observed to some extent in the deregulated US airline industry. The entry of new carriers on an airline route, in addition to multimarket contact between carriers, frequently leads to price wars. Price wars may dampen carrier profits and increase their volatility, but they also confer significant benefits on consumers.

Some industries with high fixed costs may adopt uneconomic pricing levels, at least in the short run, in situations where there is significant excess capacity (perhaps due to recession) and the process for adjusting capacity is slow or difficult. In this case, firms may price output to cover variable costs, but not average total costs. Private toll roads, especially those built at the fringe of developing urban areas, tend to have traffic levels that are sensitive to economic growth rates. Recessions can cause declines in demand that sharply lower revenues. Owners may respond by lowering toll rates to encourage traffic, since in this case significant excess capacity may exist. The revised toll rates may cover the variable costs of operating and maintaining the road, but may not contribute to recovering its fixed costs. Airlines may be vulnerable to similar types of conditions. Demand for air travel is known to be income-elastic and airlines must often place orders for new aircraft several years in advance. This combination of volatile demand and slow supply-side adjustment often leads to excess capacity during recessions. Airlines tend to respond by lowering fares in order to fill available capacity, even if the fares fall below average total cost.

Tools of Economic Regulation in Transport

The regulatory agencies are granted a broad power to regulate the following aspects of the industry:

• price regulation - maximum rate, minimum rate, rate structure
• rate-of-return regulation
• condition-of-service regulation
• entry and exit regulation
• antitrust (anti-combines) regulation including mergers and acquisition
• regulation on financial arrangements and accounting practices

Regulators may also establish safety standards, which are not discussed here.

Price Regulation

Price regulation involves the setting of limits (maximum or minimum) on the prices firms may charge for their product. In cases where prices are regulated to limit the potential abuses of monopoly suppliers, regulators may impose price-cap regulations or alternatively revenue-cap regulations. Price-cap regulations typically limit price increases to changes in economy-wide price indices (such as the consumer price index). This approach has the advantage of controlling unreasonable price increases, while retaining incentives for producers to increase profits by reducing their costs. Price regulations may also be employed to set minimum rates in cases where cut-throat competition drives prices below marginal costs for extended periods of time. Minimum rate regulations, for example, could prevent the exercise of predatory pricing in industries with few competitors.

Prior to deregulation, carriers applied to regulators for any rate change; the regulatory agency could approve, deny or vary the changes. However, generally no inflation adjustments were built into rates, and the burden was on the carrier to prove need for changes. Unjust and unreasonable rates were not allowed; e.g. youth fares could be judged as justly high, while monopoly or predatory prices could be judged as being unreasonably high or low.

Since deregulation, carriers simply file proposed fare changes, and make fares available for customers to look at. Regulator can disapprove or vary changes in 'basic fare level' upon complaints, but this rarely happens.

Rate of Return Regulation

Under rate-of-return regulation, regulatory authorities explicitly or implicitly use rate-based regulation for the carrier when they examine proposals for fare change. If the carrier made more than fair returns, fare change proposal may not get approved.

Condition of Service Regulation

Airline regulation in pre-deregulation Canada included condition-of-service regulation, which affected:

• capacity offered
• type of aircraft used
• frequency of service
• stopover condition; (e.g., PWA had to stop between Calgary and Toronto)

Entry and Exit Regulation

Regulation of entry and exit was commonplace prior to deregulation. Entry both into the industry, and onto specific routes was regulated (as was exit).

Prior to deregulation, entry of a new firm into the industry required a certificate of Public Convenience and Necessity (PCN), where burden of proof (of need for new services) was on applicant. After deregulation, new entrants needed to demonstrate they are "Fit, Willing and Able", and no longer need to show need for new service. Nevertheless, the common carrier obligation remains, and new carriers must serve all requests from public.

Entry onto routes prior to deregulation was also quite cumbersome. A route license was required for airlines and truckers. That license may have restricted carriers to certain commodities or classes of service. Since deregulation, entry onto routes was much more open.

Exit was also regulated. Prior to deregulation, it was almost impossible to abandon uneconomic routes or branchlines; therefore, carriers were required to cross-subsidize between profitable and unprofitable routes. Since deregulation, carriers can apply to the regulatory agency to abandon branchlines or exit from a route. In aviation this is straight-forward, in rail it tends to be somewhat more cumbersome. The regulatory agency either approves abandonment or gives direct subsidy to maintain uneconomic services. Usually abandonment or exit requires advance notice.

Regulation by Mode

Railway Regulation

Regulation of US railroads was initiated 1887 with the passage of the Interstate Commerce Act. The law was designed to curb the monopoly power that railroads enjoyed in many markets, with the objective of protecting shippers from paying monopoly rents. The law created a new federal regulatory agency, the Interstate Commerce Commission (ICC), which had jurisdiction over commerce taking place across state lines. Importantly, intrastate commerce issues were largely left to the states.

The Interstate Commerce Act was motivated by political pressure from the railroads' customers (primarily Western farmers) to regulate alleged monopoly abuses and collusion among several of the country's large railroads. Railroads often faced limited and inferior competition along routes and had characteristically high fixed costs, which limited the possibility of multiple railroads competing for traffic along the same route . Due to limited competition and availability of substitutes, demand for the railroads' services was price inelastic and the railroads responded by using price discrimination at stations which only they served.

The Act gave the ICC the power to set maximum rates for the railroads, while the subsequent Elkins Act required railroads to publish their rates, a provision designed to prevent them from price discriminating against similar groups of customers. Later amendments to the Act allowed for minimum, in addition to maximum, rate regulation. This provision reflected the suspicion of some ICC members that short-run marginal costs seemed too low relative to "full costs". The original Act had contained language that banned charging more for a shorter haul than a longer one. Later microeconomic research would demonstrate that the costing and rate-setting procedures of the ICC were fundamentally flawed. They reflected a misunderstanding of the relationship between costs and various types of outputs, a mistake that eventually led to uneconomic rate setting and imperiled the financial health of the industry until its deregulation in the late 1970s.

The Act also contained provisions requiring the railroads to provide services to uneconomic points, a requirement that eventually led to the practice of cross-subsidization of services.

railway monopoly in many markets: user protection need to provide services to uneconomic points: cross-subsidy some destructive competition; anti-trust need

Trucking Regulation

Started regulation in 1930s. began to question the efficacy of competition as a regulator of business; a strong push for "codes of fair competition" in society as a whole; start to regulate trucking although it was a competitive industry.

The Motor Carrier Act (MCA) of 1980 largely deregulated the interstate trucking industry in the US, reducing or eliminating most price and entry controls imposed by the federal government. Interestingly, while most federal regulatory efforts were abandoned relating to interstate trucking, states retained considerable regulatory power over the activities of intrastate truckers. Teske et al. argue that truckers turned their attention to the state level following the Motor Carrier Act, and were able to effectively capture state regulators and extract monopoly rents in what would otherwise be a competitive industry. They show that in the decade following the MCA, only eight of the 50 states had adopted legislation to loosen regulations that existed prior to 1980. Further, they argue that state-level trucking regulation is consistent with theories that emphasize regulation as serving to protect industry interests.

Airline Regulation

Started regulation in late 1930s. to help create national network subsidization of the infant industry protection from competitive entry to effect cross-subsidization (taxation by regulation - regulatory inspired cross-subsidization).

Economic regulation of airlines in the United States began in earnest in the 1930s with the passage of the Civil Aeronautics Act (CAA) of 1938. The CAA was the result of lobbying by the airlines to protect themselves from what they considered to be "excessive" competition. The CAA created a new regulatory agency, the Civil Aeronautics Authority, which was subsequently split into two separate agencies, the Civil Aeronautics Administration and the Civil Aeronautics Board (CAB), in 1940 by President Roosevelt. The former had responsibility for air traffic control, safety programs, and airway development, while the latter was responsible for safety rulemaking, accident investigation and various types of economic regulation. The CAB carried out most of the regulatory activities of the CAA, which included regulating airline fares, as well as entry into and exit from airline markets.

Entry into airline markets was limited by the CAB. It required carriers to obtain a "certificate of public convenience and necessity" (issued by the CAB) as a condition of entry in order to serve a particular route. Entry into major existing routes was difficult, as incumbent carriers often objected and appealed to the CAB. Thus, the CAB never admitted new entrants on routes that already had two or more carriers. Withdrawal of services (exit) from a route also required CAB approval. If a carrier went bankrupt, the CAB would typically arrange a merger which allowed the failing carrier to be acquired by a larger, healthier carrier (and giving the latter greater route authority in the process).

Although the CAB did not set fares directly, it did have approval power over fares filed by carriers. Since fares were set in terms of industry-wide rather than route-specific costs, the result was often fares that were much higher than costs on many routes. Airlines were not permitted to engage in price competition on routes, leading them to instead engage in intense, quality of service-based competition. The primary means for this was increases in the frequency of flights, particularly on long-distance routes. While this type of competition may have improved service quality, it also led to lower average load factors as airlines operated planes at loads substantially below capacity.

Effects of Economic Regulation

There are numerous effects of economic regulation.

Entry regulation relieves competitive pressure. Entry regulation induces x-inefficiency in the industry - gold plating, feather-bedding, etc. It was found there was a 16% cost increase due to this and crown ownership of carriers Entry regulation transfers economic rents to organized input suppliers; e.g., labor unions, aircraft manufacturers, and thereby dissipates economic rents the industry hopes to gain. Services are unresponsive to customer needs, and there are allocative inefficiencies.

Price regulations leads to excessive quality competition, see e.g., Douglas and Miller's work on airline quality competition. The system is much less flexible and far more inefficient.

Exit regulation leads to cross-subsidization from profitable to unprofitable routes. Society as a whole loses as the total welfare under cross-subsidization is lower than with direct subsidy where funds come either from government general or through air transport tax.

Rate-of-return regulations are sometimes used as a constraint to guide decisions by rate-makers concerning raising or lowering prices. That is the regulatory authority allows a fair rate of return on the value of the assets ("rate base") required to produce the services. This gives incentives for the firm to increase its "rate base" by investing more on capital input relative to labour input; In other words, the firm under rate-of-return constraint has relatively more capital vis-a-vis labor than is required to produce any given output. This is an important source of allocative inefficiency caused by the regulation. Over-capitalization, the (Averch–Johnson effect) is the tendency of companies to engage in excessive amounts of capital accumulation in order to expand the volume of their profits. If companies profits to capital ratio is regulated at a certain percentage then there is a strong incentive for companies to over-invest in order to increase profits overall.

Regulatory administration is not itself free, and this high cost needs to be considered in any analysis of welfare gains and loses from regulation. Further, regulation reduces dynamism in the industry, there are fewer innovations, which are difficult to capture in static economic analyses, yet need to be considered.

Making travel by one mode more expensive leads to a misallocation of traffic across modes, as other modes carry more traffic than a welfare analysis would suggest is optimal. These additional costs also may cause distortions elsewhere in the economy.

Note that if market failure does not exist, there is no economic need for any economic regulation. Numerous studies have investigated the effect of regulation on the airlines, highway trucking, intercity bus, and taxicab industries. In all four cases there is an ample body of empirical evidence which suggests that in the absence of regulation the market mechanism would yield an output close to a competitive equilibrium. For these industries, economic regulation has become a prime cause of market failure, far from being a remedy for market failure. Therefore, the impact of regulation on price and quantities traded in these industries can be assessed by using a competitive solution as the appropriate benchmark.

Effects of Economic Deregulation

Early economic criticisms of regulation emerged in the 1940s and 1950s; and a growing number of academic researchers criticized regulation during the 1960s. These critiques plus empirical measures of the economic cost of regulation in 1970s led to political support, and ultimately, deregulation became the default policy. Deregulation of airlines began in 1978 and railroads and trucking in 1980. The 1970s and 1980s saw a wave of deregulation across many other sectors of the US economy, in addition to substantial regulatory reforms in the transportation .

There are a couple of important points to note regarding the regulatory reforms of the 1970s and 1980s. First, most of the regulatory reforms that were undertaken addressed economic regulation, that is, regulation that directs or constrains the behavior of firms in terms of pricing, entry and exit decisions. They did not address other types of regulation such as safety, environmental, and antitrust regulation, which continued to be enforced in their previous forms and in many cases increased. Second, most of the regulatory reforms represented only partial deregulation of industries. For example, in the transportation sector prices, entry, and exit were mostly deregulated in the airline and interstate trucking industries by the early 1980s, while the ICC retained some control over railroad rate regulation. The Interstate Commerce Commission was later formally abolished in 1995, though some of its regulatory powers were transferred to a new agency, the Surface Transportation Board.

Theory of Contestable Markets

Typically, a limited number of producers in an industry (monopoly being the extreme case) is thought to lead to outcomes which deviate from the ideal of competitive markets. However, economists have more recently discovered conditions under which markets can function competitively, even in the absence of a large number of producers. Baumol, Panzar and Willig formalized the conditions under which natural monopolies could be expected to reach efficient equilibria without regulation, an idea put forward by Harold Demsetz earlier. This theory, known as the theory of contestable markets, broadened the potential areas in which the outcome of perfect competition applies. Some of the principles of contestable market theory suggest that:

• Potential competition can replace actual competition
• A single firm (monopoly) may behave like a competitive firm
• A crucial condition for a market to be contestable is free entry and exit

Levine (see page 404) identified some of the conditions considered by economists to be necessary in order for markets to be contestable. They included:

• equal access to scale economies and technology, whether expressed as access to competitive levels of unit cost or as equivalent access to product quality
• no sunk costs -- a firm can enter and exit without entry and exit costs, including operating losses resulting from predation.
• price sustainability, there is a set of prices that can occur after the entry of at least one firm which will support profitable operation.
• free entry: no entry barrier
• costless exit

The concept of contestable markets provided a broader condition supporting deregulation of transportation markets than the assumption of perfect competition. It was no longer implicitly assumed that markets in which there were not a large number of actual competitors could not function competitively in the absence regulation.

Implications for Regulation

Contestable market theory has several implications for regulation. For example, there is little need for regulation if sunk costs in an industry are low, thus regulation should be designed to focus on industries with substantial sunk costs. In that case regulation should regulate sunk facilities only and modify institutional arrangements for sunk assets. Regulators can rely on contestability theory only partially in deregulated airline markets mainly due to existence of entry barriers.

Several studies looking at the airline industry have pointed out that the airline market is only partially contestable, and that the existence of actual competition is more effective than potential competition, as determined by the overall level of welfare provided by the market. Fares in markets with potential competition were also shown to be lower than in completely monopolized markets, but higher than in markets with actual competition. The implications of these findings are that regulators should concern themselves more with fostering competition in airline markets, for example by reducing barriers to entry, in order to achieve more of the benefits from competition.

Productivity

Productivity

What is Productivity?

The question of what is productivity in transportation has several interpretations. One line of research, beginning with research by Aschauer (1988) and continuing through Boarnet (1998) and Nadiri (1996) examines how transportation investment affects the economy at large. These papers tend to treat transportation (or highways) as a black box, and make no distinctions between different kinds of transportation investment.

The input is state or national investment in transportation, and output is gross domestic product. While this research, which we refer to as macroscopic productivity provides useful rhetorical tools (transportation investments provides an X% return, compared with Y% for other investments) important for large budget debates, it provides no assistance in actually making management decisions, which requires an understanding of microscopic productivity.

Macroscopic Productivity

Theory

$GDP=f(K,L,T)$ Where:

• $GDP$ - Gross Domestic Product
• $K$ - Kapital
• $L$ - Labor
• $T$ - Transportation Investment

Evidence

Nadiri's research claims that "the average cost elasticity with respect to total highway capital for the U.S. economy during the period 1950- to 1991 is about -0.08. " That is, increasing highway investment by 1% will reduce costs by -0.08%. The average net rate of return from highway capital fell from 54% in the 1960 to 27% in the 1970s to 16% in the 1980s, the last number is close to the private rate of return, indicating a near optimal level of highway investment. Does this indicate declining productivity
 or an infrastructure shortfall? Nadiri suggests declining productivity of new investment. Aschauer argues that we are dramatically underinvested.

Thought Questions

• Which one is right?
• What do what we know about S-Curves have to say about this?

Microscopic Productivity

(based on Levinson, D. (2003a) Perspectives on Efficiency in Transportation. International Journal of Transport Management. 1 pp.145-155)

Firms try to maximize profit, society attempts to maximize overall welfare. In determining whether to build a project, select a policy, implement a system, or provide a service, it is possible to estimate the net present value of the future stream of profit or welfare with a cost/benefit analysis. However, those estimates depend on assumptions about demand and supply that may or may not pan out. For instance, the number of customers (passengers or trips, for example) depends on the money and time costs of a service, user preferences, competition or alternatives available, the availability and quality of complementary services, and other quality attributes. Money and time costs themselves depend in part on demand. User preferences and attitudes can be shaped for the better or worse depending on the service quality and number of alternatives. Competitors will emerge to provide services that replace previous needs with new ones, depending on the market strength of existing services.

Imagine a world where the only instrument your doctor had was a thermometer. He could diagnose fever, but not much else. Would you stay with him or change doctors? This is analogous to having only one Measure of Effectiveness (Consumers surplus, Benefit/Cost ratio, Volume/Capacity ratio, etc.) to understand a complex system like transportation.

Beyond Benefit/Cost

So while a benefit/cost analysis may be necessary to make good decisions, it may not be sufficient to manage a complex system such as a transportation network. Thus there is a desire to monitor the transportation network on multiple dimensions, to understand how well it is performing (and how thus accurate were previous projections), and to steer future decisions. These measures can be made at the level of a road segment or a particular transit route, or they can be appraised at the level of the local highway or transit network or technology deployed systemwide, or they can even be assessed statewide or nationally.

These metrics might assess how efficiently labor or capital is employed and change in the system (to gauge where future labor or capital will be employed). They might consider market share against competitors, the state of complementary services (for instance, access to transit or parking in the case of a transit system) or the satisfaction of customers and vendors (to gauge future market share and the price and quality of inputs).

Gauges

All of these gauges are important to monitor, but transportation in the public sector is only at the early stages of implementing such a complete management system. The most basic efficiency criteria are not routinely collected or analyzed, much less used for decisions or process improvements. While the ultimate objective in the public sector is to improve overall welfare, the difficulty is in its measurement. Things that are easily measured (flow and speed on isolated links) do not provide an unambiguous indicator of overall welfare. Better measures require much more complete (and expensive data), or models to estimate them. These better data include travel surveys, typically undertaken at most once a decade.

Definition

Productivity is a measure of output divided by input.

The larger this ratio, the more productive the system is. So either increasing output or decreasing input can increase productivity. This performance measure that can indicate the direction in which welfare is moving. All else equal, if productivity is increasing, welfare should be improving.

Example Measures

Looking at productivity in other industries may provide some guidance. Industrial productivity is an output divided by an input, for instance labor productivity would be measured as widgets per hour of labor. All else equal, a firm that produces more widgets per hour of labor will be more profitable than one which produces less. In examining a trucking firm, we may look for miles (kilometers) moved per driver-hour, basically a speed measure. Or we may want to multiply the miles (kilometers) by tons (ton-miles (kilometers)) or value (dollars). Or we may want a different denominator to get a measure of capital rather than labor productivity (number of vehicles operated).

Defining Inputs and Outputs

So the key question in measuring productivity are determining the outputs and inputs. This differs depending on what is examined. For instance, if we are considering a private bus system, then the cost of highways is paid for in taxes and fees. However if we are considering highways, we must examine the infrastructure more closely.

Inputs

Beginning with the inputs, we have, broadly, capital and labor.

• Labor includes all the workers required to produce a service paid directly by the agency, which produces that service. So when considering the productivity of transit service, labor inputs are the employees of the transit agency, including bus drivers, mechanics, managers, and accountants among others.
• Capital includes all the buildings and equipment needed to operate the service (buses, garages, offices, computers, etc).

While labor may go into each of the capital components, to the agency it is viewed as capital (the labor required to build the bus is considered in the labor productivity of the manufacturer of the bus, but not the operator).

Labor productivity ($P_{L}$) can be measured with hours of labor input (H) and an output measure (O) as:

$P_{L}={\frac {O}{H}}$

A related measure, unit labor costs (ULC) is calculated using dollars per hour, or labor compensation (C) per unit of output, represented as:

$U_{LC}={\frac {({\frac {C}{H}})}{({\frac {O}{H}})}}$

For instance, the annualized labor productivity would measure output over the year divided by total hours worked per year. The appropriate timespan depends on the case analyzed and the available data.

Similarly, capital productivity (PK) can be defined as output measure divided by the capital (K) in money terms that is required to produce that output.

$P_{K}={\frac {O}{K}}$

Capital is somewhat trickier than labor in that capital is often a stock, while output and labor are flows. For example, if it costs one million dollars to build a road section with a multi-year life, we can’t measure the productivity of capital as simply annual output divided by that one million dollars. Rather, that stock needs to be converted to a flow, as if the highway department were renting the road. This conversion depends on the interest rate and the lifespan of the facility.

Looking at either the productivity of labor or capital to the exclusion of the other is insufficient. Some investments can improve labor productivity at the expense of capital productivity. Total factor productivity measures can be used to combine labor and capital productivity. These require weights for each measure (and any submeasures which comprise a measure) proportional to the share of that measure in total costs. This issue becomes more complex when examining changes in productivity between time periods, as both inputs and outputs (and thus shares) change.

Outputs

To this point, we have been intentionally vague as to what is output in our productivity measures. What happens when a particular investment is made in transportation that actually increases overall output?

In freight, output is typically measured by something like ton-miles (kilometers) shipped. So an improvement which increases the number of ton-miles (kilometers) which can be shipped with the same resources increases productivity.

These improvements are usually timesavings (cutting distance or increasing travel speed) which enable the same truck to be used on more shipments. But they may also be the ability to ship more weight per trip or driver (for instance hauling two trailers with one tractor, or the elimination of a weight restriction because of a bridge strengthening).

Paradox  ?

It might be noted that a link that shortened the network distance traveled might not increase productivity when output is defined as ton-miles (kilometers) shipped on the network. Two effects take place. First, there is a shortening of distance, reducing ton-miles (kilometers). But there is also a shortened travel time, which may induce more trips (and thus more ton-miles (kilometers)). This paradox can be obviated by looking at point to point distance rather than network distance as the basis.

A firm relocating to be nearer its suppliers will reduce point-to-point distances. A consequence is that while total travel time may reduce, it may not reduce as fast as distance (i.e. speed may drop). Again productivity (user speed in this case) may drop, though the system is better off. Examining accessibility may be useful in this case.

Behavioral Shifts

In passenger travel, when travel times are reduced, people either travel more (either more trips or longer trips or both) or do something else with the time saved, or some combination of both. Furthermore, activity patterns may shift so trips can be taken at more convenient times of the day or by more suitable modes. Over the medium to long term, the locations of those activities may shift as well as individuals change first where they perform non-work, non-home activities such as shopping, and later may switch jobs or move homes. Trips are not goods in and of themselves, but they indicate the activities at their ends. So a new link, for instance, may increase or decrease total vehicle miles (kilometers) traveled, or total vehicle minutes of travel, but will surely result in more or different and better activities being pursued. In general, more activities can be correlated with more trip ends, though trip chaining may complicate this.

Transit

From the point of view of a transit operator, output can be measured by passenger trips or passenger miles (kilometers) carried. Which an operator desires depends on its fare structure (flat or distance based). An operator with a flat fare structure may wish (to maximize revenue, at least in the short run) to have many short trips, while with a distance-based fare structure, the operator is rewarded for longer trips. Transit operators are in many ways similar to freight haulers in the productivity sense.

Highway

A highway, on the other hand, is not so similar. Especially in the absence of link based road pricing, it is ambiguous as to what a highway operator wants to encourage to maximize overall social welfare. However, from the point of view of a link, maximizing throughput, person trips using a link or flow past a point, seems a reasonable output measure. All else equal, a link is more productive if it can serve more person trips or do so at a lower cost. Throughput cannot be maximized if service quality (travel speed) deteriorates as congestion sets in. Since the link is of a fixed length, for a given link, flow and person miles (kilometers) traveled are equivalent.

However it is important that the input and output be measured consistently. It is very hard to determine the labor required for a given link, as many services are provided network wide. If we want to consider a network, then an output measure of person miles (kilometers) traveled is necessary to allow for aggregation. An input measure of person hours traveled is useful for private time productivity. . However one element of labor that is often not considered is the time of the driver and passengers. This is especially important when we realize that the time costs to drivers and passengers dwarf those of the highway agency

Partial Productivity

Four basic partial productivity measures can thus be considered for transportation (only the first three are meaningful for transit).

Productivity of Public Labor (PGL) $P_{GL}={\frac {T}{H}}$

Productivity of Private Labor (PPL) $P_{PL}={\frac {T}{D}}$

Productivity of Public Capital (PGK) $P_{GK}={\frac {T}{K}}$

Productivity of Private Capital (PPK) $P_{PK}={\frac {T}{V}}$

Transportation planning models, such as those used by metropolitan planning organizations and others, provide data that can be used to measure productivity. In particular, over a given network, person distance traveled, person hours traveled, and dollars spent for vehicle operating costs can be estimated. Agency labor and capital costs will still need to be collected separately. But the network data can be aggregated to give us the partial private productivity measures ($P_{PL}$ and $P_{PK}$), and with the other agency data, the partial public productivity measures ($P_{GL}$ and $P_{GK}$).

Productivity of Public Labor ($P_{GL}$) $P_{GL}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{H_{l}}}}$

Productivity of Private Labor ($P_{PL}$) $P_{PL}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{D_{l}}}}$

Productivity of Public Capital ($P_{GK}$)$P_{GK}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{K_{l}}}}$

Productivity of Private Capital ($P_{PK}$)$P_{PK}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{V_{l}}}}$

Partial Factor Productivity

PFP is defined as total output / factor i. For example, a measure of PFP for labor would be Q/L where Q is total output and L is some measure of labor input such as person-hours or number of workers [note that the former measure is better since the latter assumes an equal number of hours per worker as well as equal quality of worker].

Use of PFP
The PFP measure is used quite frequently in business, particularly to measure the productivity or contribution of labor. A glance through Annual Reports from any number of industries will yield lots of evidence including those of airlines. Airports will, for example, provide measures of labor productivity of # of aircraft movements/employee or # of passengers/employee. This, perhaps, provides an excellent example of why the PFP measure is flawed; it fails to take into account other inputs such as capital which are used in the production process.

Total Factor Productivity

Total Factor Productivity (TFP) was developed to overcome the problems associated with the PFP measure. TFP takes all factor inputs into account in calculating productivity. TFP is defined as the aggregate of output over the aggregate of input. It differs from PFP in two important respects; first, it recognizes that there may be more than one output and, it recognizes all inputs in the production process.

TFP has been defined as:

$\ln \left({\frac {TFP_{K}}{TFP_{L}}}\right)=\sum \limits _{i}{\left({\frac {R_{ik}+R_{il}}{2}}\right)}\ln \left({\frac {Y_{ik}}{Y_{il}}}\right)-\sum \limits _{i}{\left({\frac {S_{ik}+S_{il}}{2}}\right)}\ln \left({\frac {X_{ik}}{X_{il}}}\right)$

where $k$ and $l$ are adjacent time periods, the $Y$'s are output indices, and the $X$'s are input indices, the $R$'s are output revenue shares, the $S$'s are input cost shares and the $i$'s denote the individual inputs or outputs. It has been shown that this equation is an exact index number to a homogeneous translog production or transformation function.

Panel Data

This definition of TFP lacks particular desirable properties if a time-series-cross sectional comparison is to be made. Since many transportation data sets form a panel (combination cross-section & time series) an alternative procedure is proposed. It is constructed in such a way as to make all bilateral comparisons both firm and time invariant. This form of TFP has been the term the "multilateral TFP index" and has been used extensively in both transportation and other industry studies to compare the performance of firms over time and against competitors. Robert Windle dealing with international comparisons of TFP used the following:

Comparing TFP

$\ln \left({\frac {TFP_{K}}{TFP_{L}}}\right)=\sum \limits _{i}{\left({\frac {R_{ik}+{\overline {R_{i}}}}{2}}\right)}\ln \left({\frac {Y_{ik}}{\overline {Y_{i}}}}\right)-\sum \limits _{i}{\left({\frac {R_{il}+{\overline {R_{i}}}}{2}}\right)}\ln \left({\frac {Y_{il}}{\overline {Y_{i}}}}\right)-\sum \limits _{i}{\left({\frac {S_{ik}+{\overline {S_{i}}}}{2}}\right)}\ln \left({\frac {X_{ik}}{\overline {X_{i}}}}\right)-\sum \limits _{i}{\left({\frac {S_{il}+{\overline {S_{i}}}}{2}}\right)}\ln \left({\frac {X_{il}}{\overline {X_{i}}}}\right)$

An important additional issue in TFP analysis is attribution of TFP. One approach has been to decompose TFP into scale effect, pricing effect and pure technological change. These are important because scale effect is due to market opportunities or managerial decisions. Pricing is also a market or managerial decision while the pure technological change effect is exogenous to the firm. Another way of attributing TFP is to take the calculated TFP index and regress it on a set of variables which describe the characteristics of the firm. An example of this procedure is contained in Gillen, Oum and Tretheway.

Revenue

Revenue and Financing

Governments, private firms, and other types of organizations that provide transportation must raise large amounts of revenue in order to pay for the construction, operation, and maintenance of transportation networks. What types of revenue sources do these organizations have available? Why are some more frequently used than others? What criteria should be used to evaluate different revenue sources? This chapter will examine these issues in more detail.

It will be useful in the discussion that follows to make a distinction between the funding and financing of transportation. These two terms are often used interchangeably in discussions though there are subtle, yet important, differences. Funding generally refers to the sources of revenue that are drawn upon to pay for transportation infrastructure and services, whereas financing tends to deal with the budgetary issues associated with matching revenues and expenditures in the provision of transportation. Most transportation infrastructure is long-lived, making the use of debt financing attractive since it allows for the conversion of one-time, fixed costs into a series of payments over time.

Revenue Sources

Over the course of history, several different types of financing mechanisms have been employed in the provision of transportation infrastructure. The following is a short, but by no means exhaustive list.

1. Direct User Charges
   1. Tolls
   2. User fees (e.g. Gas taxes, Airport facility charges, etc.)
2. Land-based Taxes
   1. Property Taxes
   2. Assessments on adjacent property
   3. Value Capture
3. General Revenue Sources
   1. Income taxes
   2. Statute labor, or the corvee, working out the road tax (a form of Poll Tax)
   3. Fines for failure to perform statute labor
   4. Sales taxes
4. Voluntary Revenue Sources
   1. Donations
   2. Private subscriptions (stock and bond sales)
   3. Public lotteries
5. Other Revenue Sources
   1. Public land sales
   2. Military Funds

Governments have many types of policy instruments at their disposal to finance and build (or encourage the development of) transportation infrastructure. There are three classes of instruments that governments typically use to accomplish this task. The first type of instrument is direct taxation or the imposition of user charges to finance infrastructure. The second and third describe, respectively, financial or regulatory incentives toward the provision of infrastructure and alternative ownership arrangements that may facilitate the private provision of infrastructure.

Direct User Charges

Taxes and tolls have played an important role in the history of transportation network development. Toll roads and bridges have a long history of use, both in North America and in Europe.

Tolls

In the 1790s, Lancaster Pike was the first significant turnpike in the US. In 1808, Albert Gallatin posited that it was legitimate for government to finance roads and developed a plan for a national network of road and canal routes linking the states of the early republic. Only roads with reasonable returns should be built, but effective transportation was seen as vital to the national defense and to national trade. On the basis of these principles, Congress had previously funded lighthouses, harbors and buoys in coastal states to facilitate trade, and authorized certain road projects, such as the National (Cumberland) Road. While the Cumberland Road Act was passed by Congress in 1806 and approved by Jefferson, authorizing the construction of a road connecting Washington, D.C. and Wheeling, Virginia (now West Virginia), on the Ohio border (thus linking the Ohio and Potomac Rivers), it largely passed because it did not present any conflict between state and federal jurisdiction because the original compact, which was made with a territory, was an undisputed federal power. Later road bills which sought to increase the scope of federal activity encountered stronger resistance as they were seen as superseding states' rights. This resistance was expressed in the debate over legislation authorizing the construction of a 1,500-mile national road linking Buffalo, New York and New Orleans, Louisiana via Washington, D.C. (which was ultimately defeated) and reaffirmed when a successive piece of legislation authorizing federal purchase of stock in a turnpike in Kentucky (the "Maysville Road") was vetoed by then-president Andrew Jackson shortly thereafter. These events solidified the notion that transportation infrastructure provision should be left to the states and the private sector until the early 20th century.

While the federal government played a comparatively small role in the development of early road networks, private individuals and associations were instrumental in financing and providing roads throughout the 19th century. Until the end of the 18th century, many roads in the early U.S. states were built and maintained by towns and counties. Westward expansion and growth within existing urban centers brought pressure for improved trade routes, many of which were financed through the formation of turnpike companies, which collected tolls from road users. Klein notes that many of the early turnpike companies were either marginally profitable or unprofitable, but nonetheless attracted private investment from many local residents. He speculates that, in many cases, the purchase of stock in turnpike companies was seen as a form of voluntary contribution toward the provision of a public good, rather than a rational investment decision. Many residents in smaller towns and cities willingly contributed and encouraged their neighbors to do likewise through the use of moral suasion, thus avoiding the free rider problem.

While turnpike companies developed networks consisting of both trunk and branch line service during the period from 1800 to 1830, the emergence of canals and railroads in subsequent decades pushed turnpikes out of the market for much long-distance travel and forced them to reorient themselves toward shorter distance travel, linking smaller towns and cities to major waterways and rail hubs. During the 1840s and early 1850s, there was also a boom in the construction of plank roads. Plank roads were financed by residents of declining rural townships, again primarily through private subscriptions to turnpike companies, and were seen as a means of connecting these places to larger markets via canal and rail networks. While plank roads appeared as a less costly alternative to railroads and conventional macadam roads, the wooden planks that were used to construct them wore out after only a few years, prompting expensive reconstruction projects for the turnpike companies who owned them. Rather than reconstruct the plank roads, many companies simply chose to abandon them or reconstruct them without planking.

The popularity of toll roads began to decline during the 1880s, coinciding with the rise of the Good Roads Movement. The Movement, initially championed by bicyclists, sought to promote improvement of the condition of roads throughout the US. European countries were often cited as examples by promoters, who saw the construction and maintenance of roads there by national and local governments as a desirable practice to be adopted in the US. The movement gained in popularity in the following decades, culminating in the passage of the Federal Road Aid Act of 1916, which established a major federal role in the financing of road improvements.

The decline of toll roads in the US was further promoted by the federal government when, during the late 1930s, the Bureau of Public Roads (precursor to the Federal Highway Administration) developed initial plans for the Interstate Highway System. Based on the findings of a 1939 report entitled Toll Roads and Free Roads authored by the BPR's Division of Information chief Herbert Fairbank, the decision was made to develop the system as a network of untolled highways. Despite this decision, some parts of the Interstate system were initially built by states as toll roads and continued to operate as toll facilities, especially in the northeastern US.

In recent years, toll roads have begun to re-emerge as an important source of revenue for transportation networks. Declines in the cost of toll collection, due to the introduction of electronic toll collection systems have made tolling a more efficient method of revenue collection than the previous generation of manual toll collection systems. Furthermore, the rapid growth of cities in Sunbelt states like California, Florida and Texas has led to an increase in toll road development to help meet increasing demand for urban travel. Most of these toll roads have been owned and operated by public or quasi-public organizations, though there are some limited examples of private toll roads in the US.

Gas Tax

The Federal Aid Road of Act of 1916 was the first piece of legislation to authorization ongoing federal support for the construction of a network of highways. The Act responded to issues of growth in automobile ownership and poor road conditions which inhibited the transport of agricultural goods to market, as well as timely delivery of mail to rural areas on post roads. Since the improvement of rural road conditions was an important focus of the program, it was initially carried out under the auspices of the Secretary of Agriculture. The matter of federal jurisdiction over the provision of interstate roads was upheld under the Interstate Commerce Clause of the US Constitution in the case of Wilson v. Shaw in 1907. The importance of the 1916 Act stemmed from the fact that it established several important components of the current federal financing system, including formula funding, the state highway organization, and the relative roles of government.

Originally, federal highway aid was paid for out of general tax revenues. In 1932 the first federal fuel tax was imposed at a rate of one cent per gallon, with the revenues deposited in the General Fund. States had preceded the federal government in adopting fuel excise taxes, with Oregon imposing the first state-level fuel tax of one cent per gallon in 1919. Other states quickly followed Oregon's lead, with all 48 states plus the District of Columbia adopting a state-level fuel tax in the following decade. State and federal fuel taxes formed the foundation of the early highway financing system, and have since remained an important part the system of transportation finance in the US. In order to fund the construction of the Interstate Highway System, Congress passed the 1956 Highway Revenue Act which established the Highway Trust Fund. Since 1956, federal fuel taxes have been directed into the Trust Fund and allocated to the states in the form of grants, rather than channeled through the General Fund. Originally the funds were dedicated to highway construction and maintenance, though more recently there have been some modifications to how the funds are distributed. The federal fuel tax has been periodically increased over time in order to keep up with the growing demand for travel.

Currently, federal fuel taxes are set at 18.4 cents per gallon, with the revenues distributed to three separate accounts. One account is dedicated to the remediation of leaky underground storage tanks at gas stations and receives 0.1 cent per gallon of the tax. The Mass Transit Account receives 2.86 cents per gallon from the tax, with the revenues used to provide grants to state and local public transit providers. The remainder of the revenues flow into the Trust Fund's Highway Account and are distributed to the states as federal highway aid. In 2008, the federal tax on gasoline raised more than $25 billion in revenue for the Highway Trust Fund. Taxes on diesel and other special fuels raised an additional $10 billion. The remaining $3 billion in revenue was collected from various other excise taxes. States also levy fuel taxes, ranging from a low of eight cents per gallon in Alaska to over 48 cents per gallon in California, with an average of 29 cents per gallon. While all states levy excise taxes on motor fuels, 35 of the 50 states also subject the sale of motor fuels to state sales taxes, though in some states motor fuels (especially gasoline) that are subject to excise taxes are exempt from sales taxation.

Range: 8 cents in Alaska to 30.8 cents in Pennsylvania (insert state gas tax table here, or graphic)

A practice in transportation finance that is relatively unique to the United States is the hypothecation (or "earmarking") of revenues from transportation taxes for the provision of transportation. In the US, revenues from federal taxes on motor fuels are dedicated to the Highway Trust Fund, where they are distributed by formula to states in the form of grants for highways, public transit, and environmental remediation. Many state and local governments in the US also apply this practice to the taxes they raise to pay for transportation services. This practice stands in contrast to many European countries, where most transportation spending is financed through general revenues and taxes on motor fuel or vehicle ownership are directed into countries' respective general funds.

Land-Based Taxes

An alternative to levying charges based on the use of transportation networks is to impose charges on the value of land or as a condition of approval to develop land. Particularly in urban areas, transportation networks provide accessibility which is valued by property owners. Locations with high levels of accessibility, such as central business districts, tend to command a premium in terms of land value. Thus, by levying charges based on the value of urban land, governments can "capture" some of the land value that flows from publicly-provided transportation networks. The set of financing mechanisms that follow this practice are often collectively referred to as value capture.

Value capture mechanisms may be particularly well-suited for use by local governments (cities, counties and some special-purpose districts), since they already make extensive use of land-based taxes for a large share of their revenue. Property taxes may be considered a type of value capture mechanism, since they are able to capture a share of the value of real property related to land. However, a more pure value capture instrument would be to adopt a land value tax, where the base of the tax was entirely dependent upon the value of land, as opposed to both the land and the buildings or other improvements built upon it. While pure land value taxes are rare (some examples are listed here, some jurisdictions in the US and elsewhere have adopted a hybrid version of the tax, known as a split-rate property tax. Some of the larger cities in the state of Pennsylvania, such as Pittsburgh, Harrisburg, and Scranton, have experimented with a split-rate tax, in which the rate of the tax on land is set higher than on improvements.

Other types of value capture mechanisms include special assessment districts, where a charge is levied on landowners within a specified geographic area near an infrastructure improvement in order to assign a share of the costs of the improvement in proportion to those who benefit. A related concept is the use of tax increment financing (TIF), where a local government issues bonds in order to finance a capital improvement, then recovers the cost of the debt over time from the increment in property taxes collected on the value of the improved property. TIF has historically been used more as a tool to promote redevelopment in economically distressed locations, but could easily be adapted for use in the context of transportation network improvements.

Value capture mechanisms may be particularly well-suited for use by public transit operators. Since the structure of public transit networks (and particularly rail networks) is such that nodes emerge in high-accessibility locations, serving as focal points for development, the increment in property value generated by the network at or near stations can be used to fund operations and perhaps some portion of capital costs. Value capture mechanisms designed around transit networks could take the form of joint development at stations, through which a private developer will either share some of the revenues from its operations or contribute toward the cost of a capital improvement, or the sale or lease of air rights above them. Some joint development agreements require developers to pay a connection charge in order to connect their proposed development to a transit station. Value capture could also take the form of special assessment or "benefit assessment" districts encompassing properties near stations that receive some special benefit.

The historical use of value capture in the United States is quite well documented and can help explain historical development patterns across the country, especially those driven by the development of railroad networks during the 19th century. The settlement of the American West was facilitated by the development of the Transcontinental Railroad, which was aided by the passage of the Pacific Railway Acts in the 1860s. Among other provisions, the laws authorized land grants to be made to the private railroads near stations in unsettled territories. The development potential of these parcels due to the increased accessibility provided by the extended rail network generated large rents for the railroads. The checkerboard pattern of development observed across the American West during this period was largely a result of the land grant policy.

Different Types of Joint Development

	Land Provision	Public			Joint			Private
	Building Provision	Public	Joint	Private	Public	Joint	Private	Public	Joint	Private
Infrastructure Provision	Public
	Joint
	Private

Joint development (of land use and infrastructure) may be joint in time and is assumed to be joint (or at least adjacent) in location. But can involve different mixes of public and private sector actors.

Development Regulation and Taxes

Local governments may also use the land development process as an opportunity to collect revenues in order to pay for transportation networks. New real estate development typically requires an extension of existing infrastructure networks or improvements in capacity. As a matter of efficiency and equity, it makes sense to allocate the costs associated with this new development proportionately to those who benefit from it. Developers are often asked to contribute toward the provision new infrastructure through impact fees or exactions. Impact fees are typically structured to recover the costs of off-site infrastructure and are often set by an explicit formula designed to estimate the costs associated with an additional resident, while exactions tend to relate to the provision of on-site infrastructure (abutting streets, etc.) and are more frequently determined through informal negotiations between a developer and the local jurisdiction responsible for development approval. Exactions can take the form of developer payments to a local government or in-kind contributions.

There are several reasons why local governments might adopt impact fees or other related taxes to recover development-related infrastructure costs. First, the imposition of impact fees to recover off-site infrastructure costs is technically straight-forward. Local governments typically set impact fees by allocating a share of the cost of off-site infrastructure to new development and estimating an "average cost" for each unit of new development. Second, the use of impact fees promotes cost sharing for infrastructure, enabling developers to share costs among several developments and thus realize whatever scale economies may exist. Third, the use of impact fees helps to minimize the costs developers face during the development process. It allows them to contribute toward the costs of development-related infrastructure they might not be able to finance on their own, but additionally it lowers development-related risk by providing an explicit process with appropriate prices to help guide developers through the approval process. Developers understand the conditions under which approval will take place, and can thus plan development schedules accordingly, with less risk of unexpected regulatory delay. This type of argument echoes the transaction cost rationale for urban land use planning activities. Impact fees tend to be limited in use to the provision of basic infrastructure and services. Their scope is limited in practice by the legal underpinnings of their constitutionality. Legal challenges to the use of impact fees have resulted the establishment of a legal rule-of-thumb that there needs to be a "rational nexus" between the level of the impact fee and the burden of infrastructure cost imposed by new development.

A variation on the impact fee concept is the formation of development districts, where developers are given permission to develop upon the condition that they pay into a fund that prospectively covers the cost of all needed infrastructure. Montgomery County, Maryland is experimenting with the development district concept as part of a revision of its zoning codes. In an attempt to encourage redevelopment at higher densities, particularly near public transit stations, the county is proposing to set up a development district near the White Flint metro station. The district would be partly funded by the county and partly by developers, and would cover the costs of urban services such as roads, sidewalks, and parks. In the case of Montgomery County, the development district is coupled with the incentive of a density bonus for developers who agree to build more densely near transit stations or to voluntarily provide other goods, such as low-cost housing. Both the development district and the density bonus provide incentives to develop more densely than existing zoning regulations allow. Thus, they may be seen as an example of regulation with loopholes to promote the provision of infrastructure by developers.

Developers may also choose to provide certain infrastructure improvements through proffers, which are essentially voluntary developer contributions toward infrastructure related to a proposed development. A developer may offer to pay for such improvements (or provide them directly) if he or she believes that the proffer will help the proposed development obtain approval more quickly. Alternatively, if the infrastructure required to serve a new development is expensive and exceeds the ability of an individual developer to finance it, multiple developers may organize a "road club", in which the developers cooperatively agree to provide the infrastructure. Typically, this involves the parties in the road club signing an agreement with the relevant jurisdiction to provide the infrastructure in exchange for collective permission to develop.

General Revenue Sources

Income Taxes

Some jurisdictions use revenues from income taxes to provide transportation services. For example, New York City's Metropolitan Transit Authority (MTA), the city's primary bus and rail transit provider, used more than $1 billion in dedicated state sales taxes to fund its operations in 2008.

Statute Labor

Some of these mechanisms, such as statute labor, date back several centuries. In Medieval Europe, the statute labor/corvee system was commonly employed under feudal systems. Feudal subjects (vassals) working in a particular fiefdom were often compelled to contribute statutory labor each year toward the construction and maintenance of road networks. The statute labor can be considered as a general revenue source in which the payments are in-kind (a crude form of the poll tax), rather than in the form of money.

Fines for Failure to Perform Statute Labor

Those who did not perform the requisite labor were often fined. Wealthier subjects could and often did pay a tax in lieu of contributing their own labor.

Sales Tax

Sales taxes are a commonly-used revenue source for transportation, especially at the local level. They are a particularly important source of revenue for local public transit systems in the US. California is a state that has extensively used sales taxes for transportation at the county level, as part of an agreement to devolve some authority over the provision of transportation to the counties. Most counties in California that have adopted sales taxes for transportation have done so through the local option process.

Voluntary Revenue Sources

Private Subscriptions

Railroads have been financed with revenues from private subscriptions, passenger fares and freight charges (the equivalent of tolls), public lotteries and land sales. The use of land-based finance mechanisms such as land sales and assessments on private property set an important precedent, as some interest in using these types of charges is returning under the concept of value capture, which will be discussed in a subsequent section.

Lotteries

In early US history, lotteries were a common means of raising revenues for public and private projects such as roads, bridges, canals, libraries and colleges. In 1768, George Washington unsuccessfully attempted to use the proceeds from the Mountain Road Lottery to build a road through the Allegheny Mountains in Virginia and to built a resort near Hot Springs, Virginia.

Incentives to build infrastructure

In addition to directly financing and building infrastructure, the public sector can offer incentives to private parties to aid in the provision of infrastructure. As mentioned previously, governments make extensive use of debt financing to pay for infrastructure. In order to make their debt more attractive to private investors, governments are able to issue many types of bonds as tax-exempt bonds, with the income from the bonds being exempt from federal taxation. This provision raises the after-tax yield of the bonds, making them more attractive to investors. In 2009, the US federal government enabled the use of Build America Bonds by state and local governments as part of the ARRA (stimulus bill). The bonds are a form of taxable municipal bond that offer a combination of tax credits and federal subsidies for issuers and bondholders. Their intended purpose is to lower the cost of borrowing for state and local governments so that they can initiate a large number of new construction projects designed to provide a fiscal stimulus.

Other types of financing incentives include government-backed bonds, where a unit of government guarantees the issuance of debt by a private entity, thus making it easier for that entity to obtain financing for a project on reasonable terms. Some private projects may be financed with private activity bonds, especially those where some element of public benefit may be determined. Private activity bonds that are qualified carry some of the same tax advantages as tax-exempt municipal bonds.

The provision of infrastructure often requires the purchase of land for right-of-way on which to build a facility. In the process of acquiring land, governments in the United States are enabled to use their powers of eminent domain when landowners will not willingly sell their land. Governments in many other countries have similar sets of powers, though they often use different terminology (e.g. "compulsory purchase" in the UK, New Zealand and Ireland). Eminent domain can serve as a powerful incentive to expedite the process of infrastructure development. Private toll roads are rare in the US, at least in part due to the difficulty of assembling contiguous parcels in developing areas. One exception was the Dulles Greenway in northern Virginia, where local landowners and governments worked cooperatively with the private developers of the road to ensure the preservation of a right-of-way over the course of the route. In contrast, most publicly-owned highways typically involve the purchase of land for right-of-way well in advance of the full development of land in a particular location. Governments seeking to accelerate the development of a new road, public or private, can use eminent domain powers to reduce delays in land acquisition.

Alternative Private Ownership of Infrastructure

In some cases it may desirable for government to encourage the private provision and ownership of infrastructure. One way to do this is to allow the private development of toll roads. Another is to allow for the private ownership and maintenance of local roads in private communities. Both of these examples are discussed in more detail in the chapter on ownership of transportation.

Other Revenue Sources

• Local Option Gas Tax, (Cooper and DePasquale 1989)
• Toll Roads, (Orange County, CA is building network)

Some other financial tools merit attention, either because they are currently in use in a number of locations or have been extensively studied and may have a larger impact on transportation finance in the future. One set of revenue sources that has significantly grown in use recently has been the adoption of local option taxes. As applied to transportation, Goldman and Wachs define local option taxes as "a tax that varies within a state, with revenues controlled at the local or regional level, and earmarked for transportation-related purposes". They identify several types of local option taxes that are applied to transportation including fuel taxes, vehicle licensing and registration taxes, general sales taxes, and income or payroll taxes. Goldman and Wachs also note the frequent association of the use of local option taxes with the adoption of direct democracy practices (e.g. initiative and referendum) and express concern over the subjugation of metropolitan transportation planning practices to popular political pressure focused on a limited set of objectives.

In the longer term, it may be desirable adopt revenue sources that are not reliant on fuel consumption as a tax base, considering the possibility of higher future energy prices and concern over environmental outcomes. One particular alternative that has received increasing attention and is anticipated to play a larger role in the future of transportation is a tax on vehicle miles traveled (VMT). As its name implies, the tax would be assessed at a specific rate and vary with the number of vehicle-miles driven. VMT taxes are envisioned as serving as a form of direct road pricing, with global positioning system (GPS) technology enabling the tracking of distance driven. Longer-term proposals for the VMT tax would attempt to differentiate the tax rate by the type of road used, by jurisdiction, and perhaps even by time of day, thus allowing for some internalization of congestion costs and making the VMT tax a closer approximation to marginal cost pricing.

The widespread adoption of a VMT tax has been limited by some political and practical considerations. Politically, there has been continued popular suspicion of the VMT tax on the grounds that it raises privacy concerns due to the use of a GPS-based system to track distance traveled. Proponents have countered this claim by mentioning that information on location does not need to be recorded and transmitted as part of the billing process. A larger issue that needs to be overcome in the development of a VMT tax, which will be discussed in the next section, is the issue of feasibility. Specifically, the collection costs for a VMT-based charging system would be high relative to existing revenue sources like motor fuels taxes. Each vehicle would need to be outfitted with a GPS unit in order to record distance and impose the appropriate charge. In the US, the vehicle fleet already numbers of in the hundreds of millions, placing the potential cost of this element of the system alone in the tens of billions of dollars.

Military Funds

The use of military funds to finance road networks was also a common occurrence in earlier civilizations (and remains to some extent today in some countries with more authoritarian regimes). Since effective road networks were often seen as a key element in the maintenance and expansion of empires (for example, the Roman Empire), large amounts of resources were often directed toward road provision under the auspices of military spending (see, for example, Berechman).

Financing Programs

The terms financing and funding are sometimes used synonymously; however in much usage, financing differs from funding revenue sources in that it is about finding money up front which will be paid back over time. When you finance a road, you may borrow funds from a source, but these funds must be paid back from a real revenue source (e.g. user fees, tolls, taxes, etc.). Traditionally in the US, municipal bonds have been used to finance infrastructure. In the US municipal bonds have the advantage of being free of Federal Income Tax. However, that is no advantage to tax exempt organizations such as pensions and foreign governments. The United States Federal Government in recent years has developed a series of other "financing tools" in addition to municipal bonds. Some of these are like municipal bonds, but present a subsidy in lieu of tax exemption (which is an implicit subsidy from the tax code). A few programs a listed below:

• Transportation Infrastructure Finance and Innovation Act (TIFIA) provides Federal credit assistance in the form of direct loans, loan guarantees, and standby lines of credit to finance surface transportation projects of national and regional significance.
• Grant Anticipation Revenue Vehicles (GARVEEs) are type of anticipation vehicle, which are securities (debt instruments) issued when moneys are anticipated from a specific source to advance the upfront funding of a particular need. In the case of transportation finance the anticipation vehicles' revenue source is expected Federal-aid grants.
• Private Activity Bonds (PAB) are tax-exempt bonds issued by state and local governments to aid in financing privately funded transportation projects.
• Build America Bonds (BAB) are tax credit bonds introduced as part of the February 2009 American Recovery and Reinvestment Act (ARRA) and are administered by the Treasury Department. A Build America Bond (BAB) is a bond issued prior to January 1, 2011 by a state or local entity for governmental purposes (non-private activity purposes) and for which the issuer elects to have the interest on the bond be taxable in return for a federal interest subsidy.
• State Infrastructure Banks (SIBs) State Infrastructure Banks are revolving infrastructure investment funds for surface transportation that are established and administered by states.

There has also been proposed an National Infrastructure Bank, which would lend money to projects (at a subsidized rate). There is some confusion about the proposed program, as some also suggest it give grants (which do not require repayment), which would make it more like a foundation than a bank which expects return on its investment. Others argue the TIFIA program already does this for transportation.

Evaluating Revenue Sources

• Evaluating Revenue Sources

Cost Allocation

• Cost Allocation

Example: Financing Transportation in Minnesota

• Example: Financing Transportation in Minnesota

Logrolling

Logrolling and vote-trading are ubiquitous aspects of public financing of infrastructure in societies governed by majoritarian politics. They are also essential to understanding how such decisions are made because simple majority decisions say nothing about the intensity of preferences. Logrolling becomes significant when minority feelings are more intense than the majority's, otherwise the majority prevails anyway. In situations where a minority group knows that elections will be held repeatedly at regular intervals, they may seek to influence outcomes on a particular issue by "buying" the support of those in the majority who hold weaker preferences, perhaps by offering support on another issue that the majority member(s) favor (a sort of quid pro quo). This type of transaction is considered to have the potential to improve social welfare, since it allows for the development of options that may make both parties, the majority and the minority, better off. Yet when allowed to proceed too far, they create other inefficiencies -- there is a finance externality.

Following Buchanan and Tullock, imagine a simple logrolling model where improvements are determined by referenda.

Imagine N farmers, each on cul-de-sac like roads A, B, and C, off of a major road. Then, consider the following two examples:

1. Each referendum to repair a single road, paid by all, fails. Farmers on roads B and C won't vote for A and vice-versa --- the result is illustrative of the outcome of a non-cooperative game.
2. Kantian road service standards, that is, when in need of repairs, any road below some threshold gets repaired. In this case, participants may behave cooperatively, though doing so may require a "Constitutional Arrangement".

Formula are possible in a narrow domain such as road repair, but much harder when comparing between domains (roads vs. education).

Logrolling often takes place in situations where jurisdictions contain multiple interest groups, each with different sets of preferences for public goods. Consider the following example.

A 2010 Wall Street Journal article highlighting the depaving of roads in some rural parts of the US described the case of Stutsman County, North Dakota. The article focused on a particular stretch of rural highway (part of what was formerly U.S. Highway 10) that was being returned to a gravel surface. The article notes that the decision to return the road to a gravel surface followed the defeat of a local referendum that, if passed, would have raised a combination of property and sales taxes within the county in order to finance road improvements. The defeat of the road tax measure (by a margin of 54 to 46 percent) represented the fourth time in 22 years that a property tax increase for road improvements was rejected by the county's voters. Notably, there was a sharp urban/rural split in the voting results, with all of the county's rural precincts voting in favor of the measure and all urban precincts (two-thirds of the county's population lives in the city of Jamestown voting against.

The closeness of the results and the geographic disparity in the voting results suggest that this situation might be one where logrolling could produce an increase in social welfare. The 46 percent of voters who favored the road tax might strongly favor the tax, while some of the 54 percent who were opposed could be convinced to change their vote if offered a better deal, for example, increased spending on parks, police protection, or other urban services. However, in this case the structure of the decision making process, namely a one-off, single-issue referendum with no guarantee of the issue being raised again in the near future, prevented such vote-trading from taking place. The result may have been different if the decision were made by a group of county commissioners through informal negotiation during the normal budget-setting process.

The Choice Between Taxes and Tolls

• The Choice Between Taxes and Tolls

Pricing

Pricing

Rationales for Pricing

Roadway congestion, air pollution from cars, and the lack of resources to finance new surface transportation options present challenges.  Road pricing, charging users a monetary toll in addition to the amount of time spent traveling, has been suggested as a solution to these problems.  While tolls are common for certain expensive facilities such as tunnels and bridges, they are less common on streets and highways.  A  new generation of private toll roads are being deployed in the United States and elsewhere.  There have been a few trials of areawide pricing schemes, such as in Singapore, London, and Stockholm, and many others proposed but not implemented.  

In short pricing can accomplish several objectives

• Revenue
• Congestion management - Traffic congestion is very common in large cities and on major highways. It is time consuming and imposes a significant amount of uncertainty and aggravation on passengers and freight transportation. Most of the cost of traffic congestion caused by travelers' selfish behaviors (see discussion of Route Choice), because they impose delays on others and do not pay the full marginal cost of their trips. In economic terms, a negative externality is created. In order to solve this problem some economist proposed that there should be a tax on congestion. In the first edition of his textbook, The Economics of Welfare, Pigou (1920) argued for a tax on congestion and thereby launched the literature on congestion pricing. Most economists support congestion pricing as a good way to relieve the dilemma, while many have been concerned about the details of implementation. Congestion charges allocate scarce road capacity in congested areas and peak times. Electronic Toll Collection (ETC) and Automated Vehicle Identification (AVI) technologies allow this to be done without delaying travelers.
• Pavement management - Pavement damage depends on vehicle weight per axle, not total vehicle weight - the damage power rises exponentially to the third power with the load per axle (e.g., a rear axle of a typical 13-ton van causes over 1000 times as much damages that of a car). In order to reflect the pavement damage costs more accurately, Small and Winston (1989) propose a "graduated per-mile tax based on axle weight". This would give truckers (truck manufactuers) an incentive to reduce axle weights by shifting to trucks with more axles, extending pavement life and reducing highway maintenance. The fuel tax currently in place provides truckers with the opposite incentives: the tax rises with a vehicle's axles, since trucks with more axles require larger engines and get lower fuel economy. They pointed out that the pavement thickness guidelines of the American Association of State Highway and Transportation Officials (AASHTO) fails to incorporate economic optimization into the design procedure. For example, by increasing rigid concrete pavement thickness only by 2.6 inches from currently 11.2 inches to 13.8 inches would more than double the life of the pavement.
• Off-loading costs or reallocating costs (changing who bears burden) - Highway cost allocation studies periodically attempt to update the amount of burden for roads borne by cars and various classes of trucks, but they only have two policy tools (gasoline and diesel fuel taxes) to do the job. A more robust pricing strategy could make charges far more directly proportional to source.
• Changing energy supply indicates declining gas tax revenue
• Encourage alternatives to driving

There are reasons that road pricing is not more widespread. Until recently, technical issues were dominant, toll collection added considerable delay and greatly reduced net revenue with the need for humans sitting in toll booths. However, advances in automatic vehicle identification and tolling have enabled toll collection, without human operators, at full speed. Other issues are fundamentally political: concerns over privacy, equity, and the perception of double taxation. Privacy concerns, though political, may have a technical solution, with the use of electronic money, which is not identified with its owner, rather than credit or debit cards or automatic identification and billing of vehicles. Equity issues, the belief that there will be winners and losers from the new system, may not be entirely resolvable. Though it can be shown that under certain circumstances road pricing has a net benefit for society as a whole, unless a mechanism exists for making a sufficient majority of road users and voters benefit, or perceive benefit, this concern is a roadblock to implementation. Similarly, people may believe that they have paid for roads already through gas taxes and general revenue, and that charging for them is akin to double taxation. Unless users can be convinced that the revenue raised is for maintenance and expansion, or another convincing public purpose, the political sell will be difficult. Widespread road pricing may require changes in the general transportation financing structure and a clear accounting of the benefits will need to be provided.

Theory of Congestion Pricing

Caption: Congestion Pricing Brings About Efficient Equilibrium.

Whenever a scarce and valued good such as road use is free or under priced, demand will outstrip supply. An illustration pertaining to road use is evident by the queues and traffic jams that occur when the number of motorists attempting to use a section of roadway at the same time exceeds the road’s capacity. Expanding capacity to meet peak demand results in wasteful excess capacity during non-peak periods unless the peak users are charged the full cost of the expansion. If we look at long-distance telephone service, allocation is determined with a market mechanism by charging a premium for a call during peak periods and by offering a discount during off peak periods. Consumers appear to accept a market-based system for allocating demand in long-distance telephone service and the system suggests this policy works.

In the case of roads, demand is allocated by congestion. The excess demand for road use during peak periods causes congestion. Economists believe that travel behavior is directed by the out-of-pocket expense of a trip plus the value of time that is required. Some motorists do shift their time of travel when congestion gets bad enough, but not enough motorists shift to entirely alleviate the congestion. The number of motorists that do shift their time of travel will never be sufficient to reduce congestion because -without some sort of pricing or rationing of road use- motorists using the road during peak periods do not have to pay for the delays they cause each other.

Making motorists pay for the delays they caused others by making their trips rather than just their personal costs would lead some to make other choices. Motorists may decide to change their time of travel, carpool, or use public transportation. Congestion pricing would allow motorists to make peak-period trips under less congested conditions, but only if they are willing to pay for the delays they impose on each other. The price would be set at a level that reduces congestion to its most efficient level, which can be shown to be the full monetary and time cost for using a segment of road capacity during the peak period.

Decisions made by road users about where and when to use their vehicles are made by comparing the benefits they will receive from using the road with the costs to themselves. These costs do not include the costs they impose on other travelers or on society as a whole, such as congestion and environmental damage. The results from this type of behavior are trips being made in which benefits to the motorist are less than the costs to society. There is more traffic than can be justified and is not efficiently located in time and capacity. If people are charged for the costs they impose on others because of their travel decisions, then that pattern of travel which results in optimal efficiently will occur.

Alternative Revenue Mechanisms

Road user charging may be more or less direct. Generally, indirect methods of road charges are related to vehicle ownership and usage. Examples would be fixed charges for owning a car -purchase tax for buying a new vehicle and annual licensing renewals- and variable charges on car usage -taxes on tires oil and fuel.

Indirect methods of road charging, such as fuel taxes, are the most commonly used in today’s society because of the high volume of usage and ease of collection. However, revenue methods like fuel taxes rarely channel funds directly into a road or transportation fund that is specifically for highway maintenance or development. Where there is congestion caused by multiple road users, drivers impose a marginal social cost in terms of delay and higher operating costs on other uses, for which they are not being charged.

Direct charging involves monitoring the actual time or distance of vehicle travel and charging appropriately. There are many ways in which to carry out direct charging. With the development of electronic technology, both off-vehicle and now in-vehicle charging mechanisms can be implemented. Off-vehicle mechanisms are devices like manual toll collection booths, coin operated machines, and road side auto-scanners. In-vehicle mechanisms are magnetic cards, smart cards, and transponders.

Congestion pricing could take several forms. The most straightforward example would be to add an extra fee to an existing toll, or to add a peak fee on an untolled route or bridge. The charge could be a simple peak premium price or off-peak discount received, or the charge could vary according to the demand imposed on a facility at a specific time.

In practice, congestion pricing could take six forms:

• Point pricing, In which a highway user passing a point at a specific time is charged a fee for passing that point regardless of the distance traveled on a specified route;
• Cordon pricing, in which users wishing to enter a congested area are charged fees at each entry point;
• Zone pricing, in which users traveling within a cordoned area also pay a fee;
• Higher charges for parking in congested areas, with particular emphasis on parking during the most congested period;
• Congestion-specific charges, in which users would be charged for both the amount of time spent and distance traveled.

The policies have different implications for demand. General taxes cannot be expected to reduce demand for travel in particular. Transportation specific taxes should reduce demand to a limited extent, but will not reduce demand on targeted road links, such as congested facilities. A cordon toll will reduce demand crossing the cordon, but by its nature is less targeted than “perfect tolls”. While different finance mechanisms have different implications for how they affect demand, they also have different costs of collection. It has historically been true that the more targeted the mechanism, the more costly. However, with the advent of wider use of electronic toll collection, those historical truisms may be altered. Varying the level of jurisdiction administering the policy changes the perception of welfare. Local governments are responsible to local citizens - their constituents, and tend not to concern themselves with the welfare of non-local residents. Therefore the incentive structure facing different layers of government needs to be distinguished. The welfare resulting from implementation when roads are owned and operated by a state may differ from the welfare if the same financing mechanism were implemented by a regional metropolitan planning organization that owned and operated the roads and could retain toll revenue. Similarly, the metropolitan planning organization differs from the county. The key reasons for these differences relate to who pays the tolls, and whether or not the (or to what extent) toll-payers reside within the boundaries of the local governmental agency. A county’s concern for the economic welfare of non-county residents is minimal, as is a metropolitan regions concern for residents of other areas. Decentralization of decision making can thus influence the chosen policy.

Effects of Congestion Pricing

The evidence from past changes in bridge and turnpike tolls demonstrates that motorists do respond to changes in price. In referring to the price elasticity of individual demand for transportation, analyses suggest an elasticity of approximately -0.10 to -0.15 as a lower limit and -0.3 to -0.4 as an upper limit depending on the charge, the current costs of travel, and the capacity of alternative roads and transit systems. There will be a decline in demand following a price increase, but consumer demand for road use is strong enough that the percentage decline in demand will not be as large as the percentage increase in price.

There are many possible changes in travel choice, including:

• Route, changing from tolled to untolled routes or to faster tolled routes.
• Time, changing to earlier or later departures to avoid tolls or tolled periods.
• Mode, changing to or away from carpools, transit, or other modes.
• Destination, changing to a closer location for non-work activities.
• Location, moving home or workplace to reduce the commute.
• Sequence, linking trips by combining multiple errands on a single trip.
• Frequency, reducing the number of less important trips
• Presence, conducting activities by telecommuting to decrease work related trips.
• Ownership, Motorists may also forgo ownership of automobiles to bypass toll charges.

Congestion pricing on highways would have broad effects on the entire transportation system by shifting the demand for transportation services away from peak period highway use by solo drivers. A reduction in the incentives to drive during peak periods would shift some traffic to the off-peak, which would increase the efficiency of the road system - therefore, reduce the demand for additional capacity. Some motorists would continue to drive during the peak but would elect to share rides with others or change the destinations of their trips. Sharing rides with others would also increase the efficiency in which the system is used by increasing the number of people per vehicle during peak periods.

Some motorists would shift to transit. The improvement in traffic flows that would result from congestion pricing would improve service reliability and speed, therefore, making transit more attractive than the automobile. The increase in use of transit would increase revenues. These revenues could be put towards increasing service frequency or route coverage. Congestion pricing would also reduce demand for new highway development. This would decrease the demand for capital expenditure on road development in response to growing population and travel demand.

Unpacking

The top part of Figure 2 shows schematically the travel time to a driver (short run average cost) at a bottleneck or on a capacitated link resulting from various levels of approach flow. The travel time function relates travel time (or delay) and approach traffic flow. The greater the approach flow, the higher the travel time. At flows below capacity (level of service A (SA) or B (SB)), traffic flows smoothly, while at high approach flows, those above capacity, traffic is stop and start and is classified as level of service E (SE) or F (SF).

The bottom part of Figure 2 shows schematically the implicit demand for travel on a link as a function of the travel time. All else equal (for instance the price charged to users), demand to travel on a link at level of service A (DA) is higher than demand at level of service F (DF). However the demand and the travel time on a link are not independent, as shown in Figure 2(A).

So the implicit demand and revealed demand are not identical, rather the revealed demand is formed by projecting the travel time at a given flow onto the implicit demand curves. So for instance, when the price charged users is high, the revealed demand coincides with the implicit demand at level of service A (DA). As the prices are lowered, the revealed demand crosses the implicit demand curve at level of service B (DB), then DC, DD, DE and finally at a zero money price it crosses DF. While the actual prices that generate specific demand levels vary from place to place with local circumstances, demand preferences, and market conditions, the general trend (higher prices gives lower approach flow gives better level of service) is simply an application of the law of demand from economics along with traffic flow theory.

In other words, the change in welfare with congestion pricing depends not only on both the change in price and quantity, but also on the change in reservation price. The reservation price is the amount travelers would be willing to pay at a given level of service. And at better levels of service, travelers (and potential travelers) have a higher reservation price.

Welfare Analysis

The movement along the revealed demand curve follows the shape of the curve shown above because of the relationship between traffic flow (quantity demanded) and travel time. Assume for instance that each level of service category represents a one-minute increase in travel time from the immediately better travel time. So in the graph, let the level of service for a one minute trip be denoted SA , and for a six minute trip, SF. The amount of traffic necessary to move from 1 minute to 2 minutes exceeds the amount to move from 2 to 3 minutes. In other words, there is a rising average (and thus marginal) cost in terms of time.

The concepts in Figure 2 can be used to develop the welfare analysis shown in Figure 3. There are several areas of interest in Figure 3. The first is defined by the lower left triangle (the blue + green) (triangle VOZ) which is the consumer surplus when the road is unpriced. The second is the producer surplus (profit) to the road authority when the road is priced, illustrated by the rectangle formed in the lower left (yellow + green) (rectangle OVWY). The third is the consumer surplus when the road is priced, shown in gray (triangle UVW). This consumer surplus represents a higher reservation price than the other because the level of service is better when flow is lower.

That first area needs to be compared to the sum of the second and third areas. If the sum of the second and third areas (OUWY) is larger than the first (OVZ), then pricing has higher welfare than remaining unpriced. Similarly, two price levels can be compared. In other words, the welfare gain from pricing is equal to the yellow + gray area (VUWX) minus the blue area (XYZ). In this particular figure, consumer’s surplus is maximized when the good is free, but overall welfare (including producer’s surplus) is not. Whether consumer’s surplus is in fact higher in a given situation depends on the slopes of the various demand curves.

The greatest welfare is achieved by maximizing the sum of the producer’s surplus rectangle and the consumer’s surplus “triangle” (it may not be a true triangle). This must recognize that the consumers surplus triangle’s hypotenuse must follow an underlying demand curve, not the revealed demand curve. Differentiating the level of service (for instance, providing two different levels of service at two different prices) may result in higher overall welfare (though not necessarily higher welfare for each individual).

Use of the Revenue

How welfare is measured and how it is perceived are two different things. If the producer’s surplus is not returned to the users of the system somehow the users will perceive an overall welfare gain as a personal loss because it would be acting as an additional tax. The money can be returned through rebates of other taxes or reinvestment in transportation. It should be noted that the entire argument can be made in reverse, where consumer and producers surplus are measured in time rather than money, and the level of service is the monetary cost of travel. This however has less practical application.

Pricing and Cost Recovery

In low volume situations, those that are uncongested, it is unlikely that the revenue from marginal cost congestion pricing will recover long term fixed costs. This is because the marginal impacts of an additional car when volume is low is almost zero, so that additional revenue which can be raised with marginal cost pricing is also zero. Imagine a road with one car - the car’s marginal impact is zero, a marginal cost price would also be zero, its revenue would thus be zero, which is less than the fixed costs.

Add a second car, and marginal impacts are still nearly zero - a phenomenon which remains true until capacity is approached.

Vickery’s Types of Congestion

• Simple interaction - light traffic, one car blocked by another, delay is proportional to Q^2
• Multiple interaction - 0.5 < V/C < 0.9

$Z=t-t_{o}=1/s-1/s_{o}=ax^{k}$

t actual time, to freeflow time, K ~ 3-5

• Bottleneck see below
• Triggerneck - overflow affects other traffic
• Network and Control - Traffic control devices transfer delay
• General Density - high traffic level in general

Marginal Cost Pricing

Transportation is a broad field, attracting individuals with backgrounds in engineering, economics, and planning, among others who don’t share a common model or worldview about traffic congestion. Economists look for received technological functions that can be analyzed, but risk misinterpreting them. Engineers seek basic economic concepts to manage traffic, which they view as their own purview. These two fields intersect in the domain of congestion pricing. However many engineers view pricing with suspicion, believing that many economists are overstating its efficacy, while the economists are frustrated with engineering intransigence, and consider engineers as lacking understanding of basic market principles.

This section applies the microscopic model of traffic congestion that to congestion pricing, and allows us to critique the plausibility of several economic models of congestion that have appeared in the literature.

This section uses the idea of queueing and bottlenecks to explain congestion. If there were no bottlenecks (which can be physical and permanent such as lane drops or steep grades, or variable such as a traffic control device, or temporary due to a crash), there would be very little congestion. Vehicles interacting on an uncongested road lead to relatively minimal delays and are not further considered (Vickery 1969, Daganzo 1995) . We define congestion, or the congested period, to be the time when there is queueing. This exceeds the time when arrivals exceed departures, as every vehicle has to wait for all previous vehicles to depart the front of the queue before it can.

A previous section developed the queueing model of congestion.

Input output diagram at level of individual vehicle

Marginal delay at level of individual vehicle

What is the implication of our queueing models for marginal cost pricing?

First, the use of hourly average time vs. flow functions such as the Bureau of Public Roads function, (which we introduced in the discussion of route choice (which approximates the hourly average delay from a queueing model) ignores that different vehicles within that hour have different travel times. They are at best useful for coarse macroscopic analyses, but should never be applied to the level of individual vehicles.

Second, travel time for a vehicle through a bottleneck depends on the number of vehicles that have come before, but not on the number of vehicles coming after. Similarly, the marginal delay that a vehicle imposes is only imposed on vehicles that come after. This implies that the first vehicle in the queue imposes the highest marginal delay, and the last vehicles in the queue have the lowest marginal delay. A marginal delay function that looks like figure on the right (bottom) is generated from the typical input-output diagram shown on the figure on the right (top). If marginal cost were equal to the marginal delay, then our pricing function would be unusual, and perhaps unstable. The instability might be tempered by making demand respond to price, rather than assuming it fixed (Rafferty and Levinson 2003), and by recognizing the stochastic nature of arrival and departure patterns, which would flatten the arrival curve to more closely resemble the departure curve, and thereby flatten the marginal delay curve.

However, the idea that the first vehicle "causes" the delay is a controversial point. Economists will sometimes argue Coase’s position (1992) – that it takes two to have a negative externality, that there would be no congestion externality but for the arrival of the following vehicles. Coase is, of course, correct. Moreover, they would note that charging a toll to the following vehicle will discourage that vehicle from coming and might also eliminate the congestion externality. This may also be true. This would however be charging the sufferer of congestion twice (once in terms of time, a second in terms of toll), while the person with the faster trip (earlier in the queue) wouldn’t pay at all. Further, it is the followers who have already internalized the congestion externality in their decision making, so tolling them is charging them twice, in contrast to charging the leaders. Given that charging either party could eliminate the externality, it would be more reasonable to charge the delayer than the delayed, which is much like the “polluter pays principle” advocated by environmentalists. It would also be more equitable, in that total costs (congestion delay + toll) would now be equalized across travelers. The disadvantage of this is that the amount of the delay caused is unknown at the time that the first traveler passes; at best it can be approximated.

Implicitly, this privileges the “right to uncongested travel” over the “right to unpriced travel”. That is a philosophical question, but given that there is to be some mechanism to finance highways, we can eliminate the notion of unpriced travel altogether, the remaining issue is how to implement financing: with insensitive prices like gas taxes or flat tolls or with time-dependent (or flow-dependent) congestion prices.

The marginal cost equals marginal delay formulation does ignore the question of schedule delay. There are practical reasons for not including schedule delay in a marginal cost price. Unlike delay, schedule delay is not easily measured. While a road administrator can tell you from traffic counts how much delay a traveler caused, the administrator has no clue as to how much schedule delay was caused. Second, if the late (early) penalty is large, then it dominates scheduling. Travelers can decide whether they would rather endure arriving early (without delay) or arriving on time, with some delay (or some combination of the two), presumably minimizing their associated costs. If they choose the delay, it is the lower cost alternative. That lower cost is the one they suffer, and thus that serves as a lower bound on the marginal cost to attribute to other travelers. If they choose schedule delay (which then becomes the cost they face) and avoid the delay, they are affected as well by other travelers, but in a way that is unknown to pricing authorities. They are “priced out of the market”, which happens all the time. In short, endogenizing schedule delay would be nice, but requires more information than is actually available.

Profit Maximizing Pricing

A realistic network of highway links is not, in the economists' terminology, perfectly competitive.  Because a link uniquely occupies space, it attains some semblance of monopoly power. While in most cases users can switch to alternative links and routes, those alternatives will be more costly to the user in terms of travel time. Theory suggests that excess profits will attract new entrants into a market, but the cost of building a new link is high, indicating barriers to entry not easily overcome.

Although roads are generally treated as public goods, they are both rivalrous when congested and in many cases excludable.  This indicates that it is feasible to consider them for privatization.  The advantages often associated with privatization are several: increasing the efficiency of the transportation system through road pricing, providing incentives for the facility operator to improve service through innovation and entrepreneurship, and reducing the time and cost of building and expanding infrastructure.

An issue little addressed is implementation. Most trials of road pricing suppose either tolls on a single facility, or area-wide control. Theoretical studies often assume marginal cost pricing on links, and don't discuss ownership structure. However, in other sectors of the economy, central control of pricing either through government ownership or regulation has proven itself less effective than decentralized control for serving customer demands in rapidly changing environments. Single prices system-wide don’t provide as much information as link-specific prices. Links which are priced only at marginal cost, the optimal solution in a first-best, perfectly competitive environment, constrain profit. While in the short-term, excess profit is not socially optimal, over the longer term, it attracts capital and entrepreneurs to that sector of the economy. New capital will both invest more in existing technology to further deploy it and enter the sector as competitors trying to gain from a spatial monopoly or oligopoly. Furthermore, new capitalists may also innovate, and thereby change the supply (and demand) curves in the industry.

By examining road pricing and privatization from a decentralized point of view, the issues associated with a marketplace of roads can be more fully explored, including short and long term distributional consequences and overall social welfare. The main contribution of this research will be to approach the problem from a theoretical and conceptual level and through the conduct of simulation experiments. This analysis will identify salient empirical factors and critical parameters that determine system performance. To the extent that available data from recent road pricing experiments becomes available, it may be used to compare with the results of the model.

Case 1. Simple Monopoly

The simplest example is that of a monopoly link, $I-J$

The link has elastic demand $Q_{d}$:

$Q_{d}=f(P)$

here given by a linear equation:

$Q_{d}=\beta _{0}-\beta _{1}P$ for all $\beta _{0}$ and $\beta _{1}>0$  

The objective of the link is to maximize profit $\pi =PQ_{d}(P)$.  Here we assume no congestion effects.  Profit is maximized when the first derivative is set to zero and the second derivative is negative. $\pi =PQ_{d}(P)=P(\beta _{0}-\beta _{1}P)=\beta _{0}P-\beta _{1}P^{2}$ Giving the following first order conditions (f.o.c.): $\delta \pi /dP=\beta _{0}-2\beta _{1}P=0$

$P=\beta _{0}/2\beta _{1}$

Checking second order conditions (s.o.c.), we find them to be less than zero, as required for a maximum.

$\delta ^{2}\pi /\delta P^{2}=-2\beta _{1}<0$

For this example, if $\beta _{0}=1000$ and $\beta _{1}=1$, $P=500$ gives $Q_{d}(P)=500$, and $profit=250,000$.  This situation clearly does not maximize social welfare, defined as the sum of profit and consumer surplus.  Consumer surplus at $P=500$ for this demand curve is 125,000, giving a social welfare (SW) of 375,000.  Potential social welfare, maximized at $P=0$ (when links are costless), would be $500,000>375,000$, all of which comes from consumer surplus.

Case 2. Monopolistic Perfect Complements

In a second simple example, we imagine two autonomous links, $I-J$ and $J-K$, which are pure monopolies and perfect complements, one cannot be consumed without consuming (driving on) the other. The links are in series.

In this case, demand depends on the price of both links, so we can illustrate by using the following general expression, and a linear example : $Q_{d}=f(P_{ij},P_{kl})$

$Q_{d}=\beta _{0}-\beta _{1}(P_{ij}+P_{jk})$

Again we assume no congestion costs.  When we profit maximize, we attain a system which produces a Nash equilibrium that is both worse off for the owners of the links, who face lower profits, and for the users of the links, who face higher collective profits, than a monopoly.  Simply put, the links do not suffer the full extent of their own pricing policy as they would in the case of a monopoly, where the pricing externality is internalized.

$\pi _{ij}=P_{ij}Q_{d}(P)=P_{ij}(\beta _{0}-\beta _{1}P_{ij}-\beta _{1}P_{jk})=\beta _{0}P_{ij}-\beta _{1}P_{ij}^{2}-\beta _{1}P_{ij}P_{jk}$

$\pi _{jk}=P_{jk}Q_{d}(P)=P_{jk}(\beta _{0}-\beta _{1}P_{ij}-\beta _{1}P_{jk})=\beta _{0}P_{jk}-\beta _{1}P_{jk}^{2}-\beta _{1}P_{ij}P_{jk}$

f.o.c. $\delta \pi /dP_{ij}=\beta _{0}-2\beta _{1}P_{ij}-\beta _{1}P_{jk}=0$

$P_{ij}=(\beta _{0}-\beta _{1}P_{jk})/2\beta _{1}$

$\delta \pi /\delta P_{jk}=\beta _{0}-2\beta _{1}P_{jk}-\beta _{1}P_{ij}=0$

$P_{jk}=(\beta _{0}-\beta _{1}P_{ij})/2\beta _{1}$

solving the f.o.c. simultaneously yields:

$P_{ij}=P_{jk}=\beta _{0}(2\beta _{1}-1)/(4\beta _{1}^{2}-\beta _{1})$

checking the s.o.c.: $\delta ^{2}\pi /\delta P_{ij}^{2}=-2\beta _{1}<0$

$\delta ^{2}\pi /\delta P_{jk}^{2}=-2\beta _{1}<0$

At $\beta _{0}=1000$ and $\beta _{1}=1$, the solution is $P_{ij}=P_{jk}=333.33$, which gives $Q_{d}(P)=333.33$, $\pi _{ij}=\pi _{jk}=111,111$, which is less total profit than the case of the simple monopoly. This situation results in total profit to both firms of 222,222, and a consumer surplus of 55,555, or total social welfare of 277,000, which is less than the results from the case of a simple monopoly. Similar arguments apply to three (or more) perfect complements, which are more and more dysfunctional if operated autonomously.  The general formula for N autonomous perfectly complementary links, with linear demand and  $\beta _{1}=1$, is given by:

$P=Q_{d}(P)=\beta _{0}/(N+1).$

Case 3. Duopoly of Perfect Substitutes

In a third example, we imagine two parallel autonomous links, $I-J$ and $K-L$, which serve the same, homogenous market.   They are perfect substitutes (operate in parallel).

The optimal pricing for this case depends upon assumptions about how users distribute themselves across suppliers and the relationships between the links.  First, assume there are no congestion costs and time costs are otherwise equal and not a factor in the decision.  Do users simply and deterministically choose the lowest cost link, or are there other factors which shape this choice, so that a minor reduction in price will not attract all users from the other link?  For this example, we assume deterministic route choice, so demand chooses the lowest cost link, or splits between the links if they post the same price.  Here, demand is defined as below:

$Q_{d}=f(P_{ij},P_{kl})$

$Q_{d}=\beta _{0}-\beta _{1}min(P_{ij},P_{kl}).$

As before, let $\beta _{0}=1000$, $\beta _{1}=1$.  Also assume that competitive links can respond instantaneously.  Assume each link can serve the entire market, so that there are no capacity restrictions. Clearly there is a (welfare maximizing) stable equilibrium at $P=0$ (assuming equal and zero costs for the links), the result for a competitive system.  Demonstration: Suppose each link sets price 500, and had 250 users.  If link IJ lowers its prices by one unit to 499, it attains all 501 users, and profits on link IJ increase to 249,999 from 125,000.  However profits on link KL drop to 0.  The most profitable decision for KL is to lower its price to 498, attain 502 users, and profits of 249,996.  This price war can continue until profits are eliminated.  At any point in the process raising prices by one link alone loses all demand.

However it seems unlikely in the case of only two links.  Therefore, if the links could coordinate their actions they would want to.  Even in the absence of formal cartels, strategic gaming and various price signaling methods are possible.   For instance, a far sighted link KL, seeing that a price war will ultimately hurt both firms, may only match the price cut rather than undercut in retaliation.  If IJ did not follow with a price cut, a price will be maintained.  It has been argued (Chamberlin 1933), that the duopoly would act as a monopoly, and both links would charge the monopoly price and split the demand evenly, because that is the best result for each since lowering prices will lead to a price war, with one link either matching or undercutting the other, in both cases resulting in smaller profits.

Case 4. Monopoly and Congestion

The previous three cases did not exploit any special features of transportation systems.  In this case travel time is introduced on the network used in Case 1.  Here demand is a function of both Price ($P$) and Time ($T$):

$Q_{d}=f(P,T)$

For this example is given by linear form:

$Q_{d}=\beta _{0}-\beta _{1}P-\beta _{2}T$

where travel time is evaluated with the following expression incorporating both distance effects and congestion (queuing at a bottleneck over a fixed period with steady demand):

if $(Q_{d}/Q_{o})<1$

$T=T_{f}$

if $(Q_{d}/Q_{o})\geq 1$

$T=T_{f}+(C/2)((Q_{d}/Q_{o})-1)$

where: $T_{f}$ = freeflow travel time, $C$ = length of congested period, $Q_{o}$ = maximum flow through bottleneck.

Because $T_{f}$ is a constant, and we are dealing with only a single link, it can be combined with $\beta _{0}$ for the analysis and won’t be considered further.  By inspection, if $Q_{o}$ is large, it too does not figure into the analysis.  From Case 1, with the $\beta$ as given, $Q_{o}$ is only important if it is less than $Q_{d}=500$.  For this example then, we will set $Q_{o}$ at a value less than 500, in this case assume $Q_{o}=250$.

As before, the objective of the link is to maximize profit $\pi =PQ_{d}(P)$. Profit is maximized when the first derivative is set to zero and the second derivative is negative.

$\pi =PQ_{d}(P)=P(\beta _{0}-\beta _{1}P-\beta _{2}T)=\beta _{0}P-\beta _{1}P^{2}-\beta _{2}P(C/2)((Q_{d}/Q_{o})-1)$

Giving the following first order conditions (f.o.c.):

$\delta \pi /dP=\beta _{0}-2\beta _{1}P-\beta _{2}(C/2)((Q_{d}/Q_{o})-1)=0$

$P=(\beta _{0}-\beta _{2}(C/2)((Q_{d}/Q_{o})-1))/(2\beta _{1})$

Solving equations (4.2) and (4.6) simultaneously, at values: $\beta _{0}=1000$, $\beta _{1}=\beta _{2}=1$, reflecting that the value of time for all homogenous travelers is 1 in the chosen unit set,  $C=1800$, representing 1800 time units (such as seconds) of congestion, we get the following answer: $P=Q_{d}=339.3,T=320.4$.   It is thus to the advantage of the monopoly in the short term, with capacity fixed, to allow congestion (delay) to continue, rather than raising prices high enough to eliminate it entirely.  In the longer term, capacity expansion (which reduces delay), will allow the monopoly to charge a higher price.  In this case,$\pi =115,600$, and $consumersurplus=57,800$.  There is a large deadweight loss to congestion, as can be seen by comparing with Case 1.

Simulation

More complex networks are not easily analyzed in the above fashion.  Links serve as complements and substitutes at the same time.  Simulation models address the same questions posed in the analytic model on more complex networks, that is, what are the performance measures and market organization under different model parameters and scenarios.  Second, we can consider market organization within the model framework, so that the question becomes: What market organization emerges under alternative assumptions, and what are the social welfare consequences of the organization?

Competing links restrict the price that an autonomous link can charge and still maximize profits.  Furthermore, it is likely that government regulations will ultimately constrain prices, though the level of regulation may provide great latitude to the owners.  It is anticipated that each link will have an objective function for profit maximization.   However, depending upon assumptions of whether the firm perfectly knows market demand, and how the firm treats the actions of competitors, the Nash equilibrium solution to the problem may not be unique, or even exist.

Because the demand on a link depends on the price of both upstream and downstream links, its complements, revenue sharing between complementary links, and the concomitant coordination of prices, may better serve all links, increasing their profits as well as increasing social welfare. Vertical integration among highly complementary links is Pareto efficient.

It is widely recognized that the roadway network is subject to economies of density, at least up to a point.  This means that as the flow of traffic on a link increases, all else equal, the average cost of operating the link declines.   It is less clear if links are subject to economies of scale, that it is cheaper per unit of output (for instance per  passenger kilometer traveled) to build and manage two links, a longer link, or a wider link than it is to build and manage a single link, a shorter link, or a narrower link.   If there are such economies of scale, then link cost functions should reflect this.

Different classes of users (rich or poor; or cars, buses, or trucks) have different values of time.  The amount of time spent on a link depends upon flow on that link, which in turn depends on price.  It may thus be a viable strategy for some links to price high and serve fewer customers with a high value of time, and others to price low and serve more customers with a lower value of time.  It is hypothesized that in a sufficiently complex network, such distinct pricing strategies should emerge from simple profit maximizing rules and limited amounts of coordination.

There are a number of parameters and rules to be considered in such simulation model, some are listed below.  

Parameters

Network Size and Shape.  The first issue that must be considered is the size of network in terms of  the number of links and nodes and how those links connect, determined by the shape of the network  (symmetric: grid, radial;  asymmetric).  While the research will begin with a small network, it is possible that the equilibrium conditions found on limited networks may not emerge on more complex networks, giving cause for considering a more realistic system.

Demand Size and Shape.  A second issue is the number of origin-destination markets served by the network, the level of demand, and the number of user classes (each with a different value of time).  Again, while the research will begin with very simple assumptions, the results under simple conditions may be very different from those under slightly more complex circumstances.

Rules

Profit Seeking.  How do autonomous links determine the profit maximizing price in a dynamic situation?   Underlying the decision of each autonomous link is an objective function, profit maximization given certain amounts of information, and a behavioral rule which dictates the amount and direction of price changes depending on certain factors.  Once a link has found a toll which it can neither raise nor lower without losing profit, it will be tempted to stick with it. However, a more intelligent link may realize that while it may have found a local maxima, because of the non-linearities comprising a complex network, it may not be at a global maxima.  Furthermore other links may not be so firmly attached to their decision, and a periodic probing of the market landscape by testing alternative prices is in order.  This too requires rules.

Revenue Sharing.  It may be advantageous for complementary links to form coalitions to coordinate their action to maximize their profit.  How do these coalition form?  By the inclusion of a share of the profits of other links in one link’s objective function, that link can price more appropriately. What level of revenue sharing, between 0 and 100 percent is best?  These questions need to be tested with the model.  An interlink negotiation process will need to be developed.

Cost Sharing. Similar to revenue sharing is the sharing of certain expenses that each link faces.  Links face large expenses periodically, such as resurfacing or snow clearance in winter, that have economies of scale.  These economies of scale may be realized either through single ownership of a great many links or through the formation of economic networks.  Just as revenue sharing between links is a variable which can be negotiated, so is cost sharing.

Rule Evaluation and Propagation.  A final set of considerations is the possibility of competition between rules.  If we consider the rules to be identified with the firms which own links or shares of links, and set pricing policy, the rules can compete.  Accumulated profits can be used by more successful rules to buy shares from less successful rules.  The decision to sell will compare future expected profits under current management with the lump sum payment by a competing firm.  An open market in the shares of links will need to be modeled to test these issues.  Similarly, it may be possible to model rules which learn, and obtain greater intelligence iteration to iteration.

Discussion

Just as airline networks seem to have evolved a hub and spoke hierarchy, a specific geometry may be optimal in a private highway network.  Initial analysis indicates that there are advantages to both the private and social welfare to vertical integration of highly complementary links.  However the degree of complementarity for which integration serves both public and private interests remains to be determined.  Other issues that are to be examined include the influence of substitutes and degree of competition on pricing policies through cross-elasticity of demand, economies of scale in the provision of infrastructure, multiple classes of users with different values of time, “free” roads competing with toll roads, and the consequences of regulatory constraints.  Using the principles developed under the analytic approach, a repeated game of road pricing by autonomous links learning the behavior of the system through adaptive expectation will be developed.

Additional Problems

• Homework

References

• Chamberlin, E (1933) "Monopolistic competition". Harvard University Press
• Coase, Ronald (1992), "The Problem of Social Cost, and Notes on the Problem of Social Cost", reprinted in The Firm, The Market and the Law, Chicago: University of Chicago Press.
• Daganzo, Carlos. (1995). An Informal Introduction To Traffic Flow Theory. University of California at Berkeley, Institute of Transportation Studies. Berkeley, CA.
• Levinson, David and Peter Rafferty (2004) Delayer Pays Principle: Examining Congestion Pricing with Compensation. International Journal of Transport Economics 31:3 295-311
• Vickrey, William (1969) Congestion Theory and Transport Investment. American Economic Review 59, pp. 251–260.

Supply chains

A supply chain can be better thought of as a web—an interconnected chain of "nodes," in this case, suppliers. In short, a supply chain is a network of distributors (of materials or finished products) and transporters (again, of materials or finished products). A supply chain may be simple or complex, depending on the situation and the industry.

Now for a general question about networks: what is the difference between economic analysis of networks and network analysis of the economy? Economic analysis of networks is required to understand and predict the deployment of advanced technologies, such as road pricing, and how those technologies interact and depend on each other. The central idea of a network is links that reinforce each other. These links can be physical (threads, wires, beams, highways, rails, pipes) or socioeconomic (kinship, social, or exchange relationships). The market, on the other hand, is a place where exchange of goods takes place. An economic network may be comprised of multiple markets. A market may sell the right to use, or the ownership of, physical networks.

Network Model of the Economy

Levinson, David and Kevin Krizek (2008) Planning for Place and Plexus: Metropolitan Land Use and Transport. Routledge

Nomenclature

Legend:

• Agent: stage s, market m, firm number n
• Open or hatched circles indicate production/consumption agent nodes
• Filled circles indicate market or exchange nodes
• Lines indicate links connection markets and agents

There are three main elements:

• the site of production/consumption (material transformation),
• the site of exchange (ownership transformation),
• and the connection between the two (spatio-temporal transformation).

While each of these elements is modeled as a link or node, it should be remembered that each can be expanded to form a subnetwork of itself if there is a desire to increase the detail or resolution of the analysis. A production/consumption agent in an economic network has both suppliers and customers, and can be modeled as an “agent node” on a network. Because production and consumption are two sides of the same coin, they are referred to together, any process consumes inputs to produce outputs. The “exchange nodes” are defined by the convergence of “connection links,” and are analogous to markets.

Linking Economy with Transportation

Clearly this situation is idealized. Some firms may have different degrees of vertical integration, that is they may internalize what is represented here as an input market or the output market. However, this figure does reflect that a production process may have economies of scope, so that a single firm produces for more than one output market, as is shown in Figure 1 between Stage 2 and Stage 3. In the illustration, there are three stages (1,2,3 from left to right) several markets in each stage (for instance a market for capital and a market for labor) and multiple firms in each market. Extending the chain far enough to the left and to the right, and incorporating enough of the economy, the markets connect with each other again, as the ultimate final consuming agent is the individual consuming goods and an ultimate input agent is an individual producing labor.

To compare with a conventional transportation network, a roadway link is a composite of the “agent node” and the “connection link”. For each link on a highway, there is only one input market and one output market, each identified with a single node (an intersection), which makes the graphic representation and analysis simpler as the agent nodes are unnecessary because the transformation is only spatial, not material. While there is “conservation of flow” in the network, flows can be one way, the link moves traffic in one direction with nothing in return. As part of a larger system, the link (more precisely, an agent: Department of Transportation, Turnpike Authority, private firm acting on behalf of the link) receives revenue from government or users, which is used to maintain the link.

Payment

In one sense, the link is selling the right to be traveled on and is paid by users or government for this right. If it is not paid, it deteriorates over time (the payment comes from the link’s own capital stock which is dissipated). The more generalized version of a graphed economy subsumes the transportation network as a special case. The use of this framework serves to incorporate, at least conceptually, financing in the standard highway network analysis, and thereby allows us to identify some pertinent issues.

In particular if we identify links with firms, the issue of payment becomes clear. In order to operate, the link must be subsidized by government, be paid for directly by users, or allow its capital stock to deteriorate. Direct payment from users equal to the marginal cost is clearly more efficient, it does not entail the social loss described in section 2 due to overuse and subsidy, and does not impose deadweight losses inherent in certain taxing structures. Imposing road pricing is a natural conclusion to these problems.

Snapshot

Figure 1 is a snapshot, it describes the processes and relationships at a given point or window of time. Over a long period of time, links and nodes are added and deleted as the economy grows and contracts, markets change, and innovation occurs in response to entrepreneurship and invention. The purpose of this analysis is to provide a tool to examine how networks and relationships in general do happen. We might extend the standard network flow idea of the least cost path to the process. Then “final” customers on the right side purchase a bundle of goods which provides the highest utility or lowest cost, profit seeking production/consumption agents in the middle will act as efficient customers for the initial producers on the left, and efficient producers/transformers in their own right. The network will generate welfare maximizing flows under the usual strong assumptions from microeconomics: well defined property rights and the absence of externalities (or when there is internalization of externalities), the presence of competitive links throughout, convex cost functions, etc. The interesting cases are in the absence of one or more of those conditions. Furthermore, the degree to which the network itself is efficient is another, much more complex (and important) question.

Supply Chains

Ram Ganeshan, Terry P. Harrison, An Introduction to Supply Chain Management

"A supply chain is a network of facilities and distribution options that performs the functions of procurement of materials, transformation of these materials into intermediate and finished products, and the distribution of these finished products to customers."

"Supply chains exist in both service and manufacturing organizations, although the complexity of the chain may vary greatly from industry to industry and firm to firm."

Single-Product Chain

Single product supply chain based on Ram Ganeshan and Terry P. Harrison

"To the right is an example of a very simple supply chain for a single product, where raw material is procured from vendors, transformed into finished goods in a single step, and then transported to distribution centers, and ultimately, customers. Realistic supply chains have multiple end products with shared components, facilities and capacities. The flow of materials is not always along an arborescent network, various modes of transportation may be considered, and the bill of materials for the end items may be both deep and large."

Supply Chain Decisions

"We classify the decisions for supply chain management into two broad categories -- strategic and operational."

• Location Decisions
• Production Decisions
• Inventory Decisions
• Transportation Decisions

Modeling Approaches

Network Design methods, for the most part, provide normative models for the more strategic decisions. Optimization of system. Inventory Control methods, on the other hand, give guiding policies for the operational decisions. These models typically assume a "single site" (i.e., ignore the network) and add supply chain characteristics to it, such as explicitly considering the site's relation to the others in the network. These derive from Inventory Control optimization Simulation methods are used to evaluate the effectiveness of a pre-specified policy rather than develop new ones. It is the traditional question of "What If?" versus "What's Best?".

Bullwhip effect

Because customer demand is rarely perfectly stable, businesses must forecast demand to properly position inventory and other resources. Forecasts are based on statistics, and they are rarely perfectly accurate. Because forecast errors are a given, companies often carry extra goods (an inventory buffer) called "safety stock" to account for and take advantage of possible unpredicted increases in demand. Moving up the supply chain from end-consumer to raw materials supplier, each supply chain participant has greater observed variation in demand and thus greater need for safety stock. In periods of rising demand, down-stream participants increase orders. In periods of falling demand, orders fall or stop to reduce inventory. The effect is that variations are amplified as one moves "upstream" in the supply chain (further from the customer).

The Beer Distribution Game, developed by the MIT Sloan School of Management in the 1960s, is an excellent simulation of the sequence of events. In the game, several teams of at least four players are in competition to meet demand for beer casings, however, only one player has knowledge of actual customer demand. Verbal communication between team members is prohibited, resulting in both massive backlogs and massive inventory buildups—the bullwhip effect, as well as frantic players.

Freight Logistics

Freight Logistics is the process of planning, implementing and controlling the efficient, effective flow and storage of raw materials, in-process inventory, finished goods, services and related information from point of origin to point of consumption to meet customer demands.

This management is increasingly important as producers move from a inventory based system (push) to a just-in-time system (pull). This is enabled by (and demands) reliable transportation and information technology. The process is multi-modal or inter-modal, that is, it uses multiple modes of transportation. Most products are loaded and unloaded multiple times at various stages within the logistics cycle.

	Value (%)	Volume (%)	$/lb	Avg Length (mi)
Trucking	72.6	52.6	$0.35	416
Railroads,	4.0	12.7	$0.08	794
Maritime,	3.9	17.2	$0.06	2300
Intermodal	10.4	1.7	$1.61
Airplanes,	2.4	0.02	$26.77	1325
Pipelines,	2.8	10.8	$0.09	825 crude, 375 other
Other	3.9	5.0	$0.20

Freight tons per capita has been increasing slowly (about 0.1% per year), but freight ton-miles has been increasing at more than 1% per year. In other words, freight being shipped farther and farther.

Railroads

Railroads move low value commodities long distances slowly (e.g. coals, chemicals, farm products), as well as large items that can't be easily or efficiently moved by truck (e.g. cars and large machinery).

Class I—major railroads

• Western (east west) Burlington Northern/Santa Fe, Union Pacific,
• Eastern (east west) CSX, Norfolk Southern,
• Central (north south) Chicago and Northwestern, Illinois Central, Kansas City Southern, Grand Trunk Western (Canadian National), and Soo Line (Canadian Pacific).

Class II—regional and short line railroads

Trucks

Trucks move higher value products short distances rapidly.

Truckload—one shipment, one truck

Less than Truckload (LTL)—multiple shippers use same truck.

Some owned by manufacturers, some by private trucking firms, some by publicly held (stock market) trucking firms.

Small trucks are often used as private vehicles, so truck statistics need to be considered with care. Almost 60,000,000 trucks in United States.

Low Cost Envelope

Which mode is selected depends on which mode has the lowest cost, typically this can be illustrated with the low cost envelope:

Production

Production

Introduction

Transportation inputs and outputs

Transportation moves people and goods from one place to another using a variety of vehicles across different infrastructure systems. It does this using not only technology (namely vehicles, energy, and infrastructure), but also people’s time and effort; producing not only the desired outputs of passenger trips and freight shipments, but also adverse outcomes such as air pollution, noise, congestion, crashes, injuries, and fatalities.

Figure 1 illustrates the inputs, outputs, and outcomes of transportation. In the upper left are traditional inputs (infrastructure (including pavements, bridges, etc.), labor required to produce transportation, land consumed by infrastructure, energy inputs, and vehicles). Infrastructure is the traditional preserve of civil engineering, while vehicles are anchored in mechanical engineering. Energy, to the extent it is powering existing vehicles is a mechanical engineering question, but the design of systems to reduce or minimize energy consumption require thinking beyond traditional disciplinary boundaries.

On the top of the figure are Information, Operations, and Management, and Travelers’ Time and Effort. Transportation systems serve people, and are created by people, both the system owners and operators, who run, manage, and maintain the system and travelers who use it. Travelers’ time depends both on freeflow time, which is a product of the infrastructure design and on delay due to congestion, which is an interaction of system capacity and its use. On the upper right side of the figure are the adverse outcomes of transportation, in particular its negative externalities:

• by polluting, systems consume health and increase morbidity and mortality;
• by being dangerous, they consume safety and produce injuries and fatalities;
• by being loud they consume quiet and produce noise (decreasing quality of life and property values); and
• by emitting carbon and other pollutants, they harm the environment.

All of these factors are increasingly being recognized as costs of transportation, but the most notable are the environmental effects, particularly with concerns about global climate change. The bottom of the figure shows the outputs of transportation. Transportation is central to economic activity and to people’s lives, it enables them to engage in work, attend school, shop for food and other goods, and participate in all of the activities that comprise human existence. More transportation, by increasing accessibility to more destinations, enables people to better meet their personal objectives, but entails higher costs both individually and socially. While the “transportation problem” is often posed in terms of congestion, that delay is but one cost of a system that has many costs and even more benefits. Further, by changing accessibility, transportation gives shape to the development of land.

Transportation and Production

Transportation is a process of production as well as being a factor input in the production function of firms, cities, states and the country. Transportation is produced from various services and is used in conjunction with other inputs to produce goods and services in the economy. Transportation is an intermediate good and as such has a "derived demand". Production theory can guide our thinking concerning how to produce transportation efficiently and how to use transportation efficiently to produce other goods.

More broadly, one has transportation as an input into a production process. For example, the Gross National Product (GNP) of the economy is a measure of output and is produced with capital, labor, energy, materials and transportation as inputs. GNP = f(K, L, E, M, T)

Alternatively we can view transportation as an output: e.g. passenger-miles of air service, ton-miles of freight service or bus-miles of transit service. These outputs are produced with inputs including transportation.

T = g(K, L, E, M,)

We will focus on the latter view in this chapter.

Production processes involve very large numbers of inputs and outputs. It is usually necessary to aggregate these in order to keep the analysis manageable; examples would include types of labor and types of transportation.

Measuring inputs and outputs

• material inputs -- volume/mass
• human inputs--labor and users (time)
• service inputs - navigation, terminal operations
• capital inputs - physical units, monetary units (stocks & flows)
• design inputs - dimensions, weight, power
• transportation - cargo trips, vehicle trips, vehicle miles, capacity miles, miles

Characterizing Transportation Production

Design Parameters in Transportation

In transportation, output is a "service" rather than product. It is not storable (capacity unused now cannot be sold later, this leads to the economics of peak/off-peak) and users participate in the production (passengers are key elements in producing the output).

Inputs are supplied by carriers, users, and public:

• carriers: terminal activities, line haul activities, etc.
• users: the value of time, etc.
• public: infrastructure

Production is characterized by multidimensional (heterogeneous) outputs.

• quantity: most common measures of outputs;
  • tonne-kilometres
  • passenger-kilometres
• spatial dimension - origin-destination and direction
• time dimension - transit time, peaking and seasonality
• quality of service - speed, reliability, etc.

Examples of the use of the production approach for system design considering both inputs and outputs are illustrated in the following table:

Inputs	Outputs
dimensions	surface area/volume carrying capacity
size, speed	transport capacity (e.g. vehicles per hour)
system capacity, infrastructure quality	traffic flow
capacity, vehicle movements	O-D trips
runways, terminals	passenger and aircraft movements

Lumpy investments refer to indivisibility of investments leads to complex costing and pricing. E.g you cannot build half a lane or half a runway and have it be useful.

Sunk investments can constitute an entry barrier.

Joint production occurs when it is unavoidable to produce multiple outputs in fixed proportions, e.g. fronthaul-backhaul problem; there is a joint cost allocation problem. Joint costs are where the multiple products are in fixed invariant proportions.

In common production, multiple outputs of varying proportions are produced using same equipment or facility - cost saving benefits, e.g. freight and passenger services using a same airplane, or using a same train. Common costs are where multiple services can be produced in variable proportions for the same cost outlay

Carriers have a structure that can be decomposed into two primary activities (Terminal and Linehaul)

Terminal activities include loading, unloading and sorting of goods (and, perhaps, pick up and delivery). The concept of speed can be important for terminals, while distance to be travelled is only of limited relevance. Terminal activities may differ depending upon the type of cargo., e.g. we see increasing returns to scale for bulk loading facilities, while it is not clear whether or not there are increasing returns to scale for facilities handing diverse product types.

Linehaul activities exhibit indivisibility of output unit on the supply side due to:

• lumps of capacity and nonstorability of output (mismatch between demand and production quantity)
• joint production of backhaul capacity
• common production; e.g., short haul markets served in conjunction with a longer haul market.

Production Theory

Production function

Isoquants

Theory of production analyzes how a firm, given the given technology, transform its inputs ($x$) into outputs ($y$) in an economically efficient manner. A production function, $y=f(x)$, is used to describe the relationship between outputs and inputs.

Efficiency

X-Efficiency is the effectiveness with which a given set of inputs are used to produce outputs. If a firm is producing the maximum output it can given the resources it employs, it is X-efficient.

Allocative efficiency is the market condition whereby resources are allocated in a way that maximizes the net benefit attained through their use. In a market under this condition it is impossible for an individual to be made better off without making another individual worse off.

Technical efficiency refers to the ability to produce a given output with the least amount of inputs or equivalently, to operate on the production frontier rather than interior to it.

Production Possibilities Set

Production possibilities set

The Production Possibilities Set is the set of feasible combinations of inputs and outputs. To produce a given number of passenger trips, for example, planes can refuel often and thus carry less fuel or refuel less often ands carry more fuel. Output is vehicle trips, inputs are fuel and labor.

If the production possibilities set (PPS) is convex, it is possible to identify an optimal input combination based on a single condition. However, if the PPS is not convex the criteria becomes ambiguous. We need to see the entire isoquant to find the optimum but without convexity we can be 'myopic', as illustrated on the right.

linear homogeneous in input prices

$C\left(Q,2P_{1},2P_{2}\right)=2C\left(Q,P_{1},P_{2}\right)$

marginal cost is positive for all outputs

${\frac {\partial C}{\partial Q_{j}}}>0\forall j$.

The derivative of the cost function with respect to the price of an input yields the input demand function.

${\frac {\partial C}{\partial P_{j}}}=X\left(\bullet \right)$

As input prices rise we always substitute away from the relatively more expensive input.

${\frac {\partial ^{2}C}{\partial P_{i}^{2}}}\leq 0\forall i$

Functional Forms

Production functions are relationships between inputs and outputs given some technology. A change in technology can affect the production function in two ways. First, it can alter the level of output because it affects all inputs and, second, it can increase output by changing the mix of inputs. Most production functions are estimated with an assumption of technology held constant. This is akin to the assumption of constant or unchanging consumer preferences in the estimation of demand relationships.

The functional form represents the inputs are combined. These can range from a simple linear or log-linear (Cobb-Douglas) relationship to a the second order approximation represented by the 'translog' function.

Linear

A linear production function is the simplest:

$Y=A+\alpha L+\beta K$

Quadratic

A quadratic production function adds squares and interaction terms.

$Y=A+\alpha L+\beta K+\gamma L^{2}+\phi K^{2}+\rho KL$

Cobb-Douglas

(adapted from Wikipedia article on the Cobb Douglas function )

For production, the Cobb-Douglas function is

$Y=AL^{\alpha }K^{\beta },$

where:

• Y = total production (the monetary value of all goods produced in a year)
• L = labor input
• K = capital input
• A = total factor productivity
• $\alpha$ and $\beta$ are the output elasticities of labor and capital, respectively. These values are constants determined by available technology.

Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. For example if $\alpha =0.15$, a 1% increase in labor would lead to approximately a 0.15% increase in output.

Further, if:

$\alpha +\beta =1$

the production function has constant returns to scale. That is, if L and K are each increased by 20%, Y increases by 20%. If

$\alpha +\beta <1$

returns to scale are decreasing, and if

$\alpha +\beta >1$

returns to scale are increasing. Assuming perfect competition and$\alpha +\beta =1$ , $\alpha$ and $\beta$ can be shown to be labor and capital's share of output.

Translog

The translog production function is a generalization of the Cobb–Douglas production function. The name translog stands for 'transcendental logarithmic'.

The two-factor translog production function is:

${\begin{aligned}\ln(Y)&=\ln(A)+a_{L}\ln(L)+a_{K}\ln(K)+b_{LL}\ln(L)\ln(L)\\&{}\qquad {}+b_{KK}\ln(K)\ln(K)+b_{LK}\ln(L)\ln(K)\\&=f(L,K).\end{aligned}}$

where L = labor, K = capital, and Y = product.

CES (constant elasticity of substitution)

Constant elasticity of substitution (CES) function: $Y=A[\alpha K^{\gamma }+(1-\alpha )L^{\gamma }]^{\frac {1}{\gamma }}$

$\gamma =0$ corresponds to a Cobb–Douglas function, $Y=AK^{\alpha }L^{1-\alpha }$

Leontief

The Leontief production function applies to situations in which inputs must be used in fixed proportions; starting from those proportions, if usage of one input is increased without another being increased, output will not change. This production function is given by

$Y=\min(aK,\ \ bL,\ \ ...).$

Characteristics of a Production Function

Production Function

The examination of production relationships requires an understanding of the properties of production functions. Consider the general production function which relates output to two inputs (two inputs are used only for exposition and the conclusions do not change if more inputs or outputs are considered, it is simply messier)

$Q=f(K,L)$

Consider fixing the amount of capital at some level and examine the change in output when additional amounts of labor (variable factor) is added. We are interested in the $\Delta Q/\Delta L$ which is defined as the marginal product of labor and the $Q/L$ the average product of labor. One can define these for any input and labor is simply being used as an example.

This is a representation of a 'garden variety' production function. This depicts a short run relationship. It is short run because at least one input is held fixed. The investigation of the behavior of output as one input is varied is instructive.

Note that average product (AP) rises and reaches a maximum where the slope of the ray, $Q/L$ is at a maximum and then diminishes asymptotically.

Marginal product (MP) rises (area of rising marginal productivity), above AP, and reaches a maximum. It decreases ( area of decreasing marginal productivity) and intersects AP at AP's maximum . MP reaches zero when total product (TP) reaches a maximum. It should be clear why the use of AP as a measure of productivity (a measure used very frequently by government, industry, engineers etc.) is highly suspect. For example, beyond $MP=0$, $AP>0$ yet TP is decreasing.

The principle of "diminishing marginal productivity " is well illustrated here. This principle states that as you add units of a variable factor to a fixed factor initially output will rise, and most likely at an increasing rate but not necessarily) but at some point adding more of the variable input will contribute less and less to total output and may eventually cause total output to decline (again not necessarily).

Any shifts in the fixed factor (or technology) will result in an upward shift in TP, AP and MP functions. This raises the interesting and important issue of what it is that generates output changes; changes in variable factors, technology and/or changes in technology.

Isoquants

Isoquants

Two Isoquants (Corner and Interior Solutions)

The isoquant reveals a great deal about technology and substitutability. Like indifference curves, the curvature of the isoquants indicate the degree of substitutability between two factors. The more 'right-angled' they are the less substitution. Furthermore, diminishing marginal product plays a role in the slope of the isoquant since as the proportions of a factor change the relative Marginal Product's change. Therefore, substitutability is simply not a matter of the technology of production but also the relative proportions of the inputs.

Rather than consider one factor variable, consider two (or all) factors variable.

$Q=f(K,L)$.

Taking the total derivative and setting equal to zero

$dQ={\frac {\partial f}{\partial K}}dK+{\frac {\partial f}{\partial L}}dL=0$

rearranging one can see that the ratio of the marginal productivities (${\frac {MP_{K}}{MP_{L}}}$) equals ${\frac {dk}{dL}}$

Equivalently, the isoquant is the locus of combinations of K and L which will yield the same level of output and the slope (${\frac {dk}{dL}}$) of the isoquant is equal to the ratio of marginal products.

The ratio of MP's is also termed the "marginal rate of technical substitution " MRTS.

As one moves outward from the origin the level of output rises but unlike indifference curves, the isoquants are cardinally measurable. The distance between them will reflect the characteristics of the production technology.

The isoquant model can be used to illustrate the solution of finding the least cost way of producing a given output or, equivalently, the most output from a given budget. The innermost budget line corresponds to the input prices which intersect with the budget line and the optimal quantities are the coordinates of the point of intersection of optimal cost with the budget line. The solution can be an interior or corner solution as illustrated in the diagrams below.

Constrained Optimization

An example of this constrained optimization problem just illustrated is:

${\begin{aligned}&{\text{Min cost }}={\text{ }}p_{1}x_{1}+p_{2}x_{2}\\&{\text{s}}{\text{.t}}{\text{. }}F(x_{1},x_{2})=Q\\\end{aligned}}$

where

• f() is the production function
• Objective function (Min cost): desire
• Constraint (subject to): necessity
• $x_{1},x_{2}$: decision variables

The method of Lagrange Multipliers is a method of turning a constrained problem into an unconstrained problem by introducing additional decision variables. These 'new' decision variables have an interesting economic interpretation.

${\begin{aligned}&{\text{Max }}g\left({\bar {x}}\right)\\&{\text{s}}{\text{.t}}{\text{. }}h_{j}\left({\bar {x}}\right)=b_{j}\\\end{aligned}}$

Lagrangian:

${\text{Max}}\Lambda \left({\bar {x}},{\bar {\lambda }}\right)=g\left({\bar {x}}\right)-\sum {{\bar {\lambda }}_{j}\left(h_{j}\left({\bar {x}}\right)-b_{j}\right)}$

To find the maximum, take the first derivative and set equal to zero

${\frac {\partial \Lambda }{\partial x_{i}}}={\frac {\partial g}{\partial x_{i}}}-\sum \limits _{j}{\lambda _{j}}{\frac {\partial h_{j}}{\partial x_{i}}}=0$

${\frac {\partial \Lambda }{\partial \lambda _{j}}}=-h_{j}\left(x\right)+b_{j}=0$

1. Lagrangian is maximized (minimized)
2. Lagrangian equals the original objective function
3. constraints are satisfied

Lagrange multipliers represent the amount by which the objective function would change if there were a change in the constraint. Thus, for example, when used with a production function, the Lagrangian would have the interpretation of the 'shadow price' of the budget constraint, or the amount by which output could be increased if the budget were increased by one unit, or equivalently, the marginal cost of increasing the output by a unit.

Example

${\begin{aligned}&{\text{Min cost }}={\text{ }}p_{1}x_{1}+p_{2}x_{2}\\&{\text{s}}{\text{.t}}{\text{. }}F(x_{1},x_{2})=Q\\\end{aligned}}$

$\Lambda =p_{1}x_{1}+p_{2}x_{2}-\lambda (F(x_{1},x_{2})-Q)$

${\frac {\partial \Lambda }{\partial x_{1}}}=-p_{\text{1}}-\lambda {\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{\text{1}}}}=0$

${\frac {\partial \Lambda }{\partial x_{2}}}=-p_{\text{2}}-\lambda {\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{\text{2}}}}=0$

${\frac {\partial \Lambda }{\partial \lambda _{j}}}=Q-F\left(x_{\text{1}},x_{\text{2}}\right)=0$

${\frac {p_{\text{1}}}{\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{\text{1}}}}}=\lambda$

${\frac {p_{2}}{\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{2}}}}=\lambda$

${\frac {p_{\text{1}}}{p_{2}}}={\frac {\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{\text{1}}}}{\frac {\partial F\left(x_{\text{1}},x_{\text{2}}\right)}{\partial x_{2}}}}$

so

$\lambda ={\frac {\partial \Lambda }{\partial Q}}$

is equal to the marginal cost of output.

Conditions

First order conditions (FOC) are not sufficient to define a minimum or maximum.

The second order conditions are required as well. If, however, the production set is convex and the input cost function is linear, the FOC are sufficient to define the maximum output or the minimum cost.

Optimization

Production expansion path

A profit maximizing firm will hire factors up to that point at which their contribution to revenue is equal to their contribution to costs. The isoquant is useful to illustrate this point.

Consider a profit maximizing firm and its decision to select the optimal mix of factors.

$\Pi =Pf\left(K,L\right)-\left(wL+rK\right)$

${\frac {\partial \Pi }{\partial K}}=P{\frac {\partial f}{\partial K}}-r=0$

${\frac {\partial \Pi }{\partial L}}=P{\frac {\partial f}{\partial L}}-w=0$

This illustrates that a profit maximizing firm will hire factors until the amount they add to revenue [marginal revenue product] or the price of the product times the MP of the factor is equal to the cost which they add to the firm. This solution can be illustrated with the use of the isoquant diagram.

The equilibrium point, the optimal mix of inputs, is that point at which the rate at which the firm can trade one input for another which is dictated by the technology, is just equal to the rate at which the market allows you to trade one factor for another which is given by the relative wage rates. This equilibrium point, should be anticipated as equivalent to a point on the cost function. Note that this is, in principle, the same as utility pace and output space in demand. It also sets out an important factor which can influence costs; that is, whether you are on the expansion path or not.

In order to move from production to cost functions we need to find the input cost minimizing combinations of inputs to produce a given output. This we have seen is the expansion path. Therefore, to move from production to cost requires three relationships:

1. The production function
2. The budget constraint
3. The expansion path

The 'production cost function' is the lowest cost at which it is possible to produce a given output.

Duality

There is a duality between the production function and cost function. This means that all the information contained in the production function is also contained in the cost function and vice-versa. Therefore, just as it was possible to recover the preference mapping from the information on consumer expenditures it is possible to recover the production function from the cost function.

Suppose we know the cost function C(Q,P') where P" is the vector of input prices. If we let the output and input prices take the values C˚, P˚1 and P˚2, we can derive the production function.

1. Knowing specific values for output level and input prices means that we know the optimal input combinations since the slope of the isoquant is equal to the ratio of relative prices.

2. Knowing the slope of the isoquant we know the slope of the budget line

3. We know the output level.

We can therefore generate statements like this for any values of Q and P's that we want and can therefore draw the complete map of isoquants except at input combinations which are not optimal.

Factor Demand Functions

Factor Demand Function

One important concept which comes out of the production analysis is that the demand for a factor is a derived demand; that is, it is not wanted for itself but rather for what it will produce. The demand function for a factor is developed from its marginal product curve, in fact, the factor demand curve is that portion of the marginal product curve lying below the AP curve. As more of a factor is used the MP will decline and hence move one down the factor demand function. If the price of the product which the factor is used to produce the factor demand function will shift. Similarly technological change will cause the MP curve to shift.

Input Cost Functions

Input Cost Function

Recall that our production function Q = f(x1, x2) can be translated into a cost function so we move from input space to dollar space. the production function is a technical relationship whereas the cost function includes not only technology but also optimizing behavior.

The translation requires a budget constraint or prices for inputs. There will be feasible non-optimal combinations of inputs which yield a given output and a feasible-optimal combination of inputs which yield an optimal solution.

Technical Change

Technical Change

Technical change can enter the production function in essentially three forms; secular, innovation and facility or infrastructure.

Technical change can affect all factors in the production function and thus be 'factor neutral' or it may affect factors differentially in which case it would be 'factor biased'.

The consequence of technical change is to shift the production function up (or equivalently, as we shall see, the cost function down), it can also change the shape of the production function because it may alter the factor mix.

This can be represented in an isoquant diagram as indicated on the right.

If relative factor prices do not change, the technical change may not result in a new expansion path, if the technical change is factor neutral, and hence it simply shifts the production function up parallel. If the technical change is not factor neutral, the isoquant will change shape, since the marginal products of factors will have changed, and hence a new expansion path will emerge.

Types of Technical Change:

• secular - include time in production function
• innovation - include presence of innovation in production function
• facility - include availability of facility in production function

Conditions

First order conditions (FOC) are not sufficient to define a minimum or maximum.

The second order conditions are required as well. If, however, the production set is convex and the input cost function is linear, the FOC are sufficient to define the maximum output or the minimum cost.

Costs

Costs

Introduction

Price, cost and investment issues in transportation garner intense interest. This is certainly to be expected from a sector that has been subject to continued public intervention since the ninteenth century. While arguments of market failure, where the private sector would not provide the socially optimal amount of transportation service, have previously been used to justify the economic regulations which characterized the airline, bus, trucking, and rail industries, it is now generally agreed, and supported by empirical evidence, that the move to a deregulated system, in which the structure and conduct of the different modes are a result of the interplay of market forces occurring within and between modes, will result in greater efficiency and service.

Many factors have led to a reexamination of where, and in which mode, transportation investments should take place. First, and perhaps most importantly, is the general move to place traditional government activities in a market setting. The privatization and corporatization of roadways and parts of the aviation systems are good examples of this phenomenon. Second, there is now a continual and increasing fiscal pressure exerted on all parts of the economy as the nation reduces the proportion of the economy’s resources which are appropriated by government. Third, there is increasing pressure to fully reflect the environmental, noise, congestion, and safety costs in prices paid by transportation system users. Finally, there is an avid interest in the prospect of new modes like high speed rail (HSR) to relieve airport congestion and improve in environmental quality. Such a major investment decision ought not be made without understanding the full cost implications of a technology or investment compared to alternatives.

This chapter introduces cost concepts, and evidence on internal costs. The chapter on Negative externalities reviews external costs.

Supply

In imperfectly competitive markets, there is no one-to-one relation between P and Q supplied, i.e., no supply curve. Each firm makes supply quantity decision which maximises profit, taking into account the nature of competition (more on this in pricing section).

Supply function (curve). specifies the relationship between price and output supplied in the market. In a perfectly competitive market, the supply curve is well defined. Much of the work in transportation supply does not estimate Supply-curve. Instead, focus is on studying behaviour of the aggregate costs (in relation to outputs) and to devising the procedure for estimating costs for specific services (or traffic). Transport economists normally call the former as aggregate costing and the latter as disaggregate costing. For aggregate costing, all of the cost concepts developed in micro-economics can be directly applied.

Types of Costs

There are many types of costs. Key terms and brief definitions are below.

• Fixed costs ($C_{F}$): The costs which do not vary with output.
• Variable costs ($C_{V}$): The costs which change as output levels are changed. The classification of costs as variable or fixed is a function of both the length of the time horizon and the extent of indivisibility over the range of output considered.
• Total costs ($C_{T}$): Total expenditures required to achieve a given level of output ($Q$).
  • Total costs = fixed costs + variable costs. = a + bQ
• Average costs: The total cost divided by the level of output.
  • Average Cost for a single product firm: $C_{A}=C_{T}/Q$,
    • Average fixed cost = $a/Q$
    • Average variable cost = $b$
  • Average Cost for a multi-product firm is not obvious (i.e. which output), two methods
    • Ray average cost: Fix the output proportion and then examine how costs change as the scale of output is increased along the output 'ray'. Like moving out along a ray in output space - thus 'ray' average cost; multiproduct scale economies exists if there is DRAC (declining ray average cost). (Fixity or Variability depends on the time horizon of the decision problem and is closely related to the indivisibility of production (costs).)
    • Incremental average cost: Fix all other output except one, and then examine the incremental cost of producing more ith output - thus, incremental average cost; product-specific scale economies exist if there is DAIC (declining average incremental cost).
• Marginal (or incremental) cost: The derivative (difference) of Total Cost with respect to a change in output.
  • Marginal Cost MC = $dC_{T}/dQ$
  • Incremental Cost IC = $\Delta C_{T}/\Delta Q$
• Opportunity costs: The actual opportunities forgone as a consequence of doing one thing as opposed to another. Opportunity cost represents true economics costs, and thus, must be used in all cases.
• Social cost: The cost the society incurs when its resources are used to produce a given commodity, taking into account the external costs and benefits.
• Private cost: The cost a producer incurs in getting the resources used in production.

Shared costs

The production of transport services in most modes involves joint and common costs. A joint cost occurs when the production of one good inevitably results in the production of another good in some fixed proportion. For example, consider a rail line running only from point A to point B. The movement of a train from A to B will result in a return movement from B to A. Since the trip from A to B inevitably results in the costs of the return trip, joint costs arise. Some of the costs are not traceable to the production of a specific trip, so it is not possible to fully allocate all costs nor to identify separate marginal costs for each of the joint products. For example, it is not possible to identify a marginal cost for an i to j trip and a separate marginal cost for a j to i trip. Only the marginal cost of the round trip, what is produced, is identifiable.

Common costs arise when the facilities used to produce one transport service are also used to produce other transport services (e.g. when track or terminals used to produce freight services are also used for passenger services). The production of a unit of freight transportation does not, however, automatically lead to the production of passenger services. Thus, unlike joint costs, the use of transport facilities to produce one good does not inevitably lead to the production of some other transport service since output proportions can be varied. The question arises whether or not the presence of joint and common costs will prevent the market mechanism from generating efficient prices. Substantial literature in transport economics (Mohring, 1976; Button, 1982; Kahn, 1970) has clearly shown that conditions of joint, common or non-allocable costs will not preclude economically efficient pricing.

• Traceable cost (untraceable cost): A cost which can (cannot) be directly assigned to a particular output (service) on a cause-and-effect basis. Traceable (untraceable) costs may be fixed or variable (or indivisible variable). Traceability is associated with production of more than one output, while untraceable costs possess either (or both) common costs and joint costs. The ability to identify costs with an aggregate measure of output supplied (e.g. the costs of a round trip journey) does not imply that the costs are traceable to specific services provided.
• Joint cost: A cost which is incurred simultaneously during the production for two or more products, where it is not possible to separate the contributions between beneficiaries. These may be fixed or variable (e.g. cow hides and cow steaks).
• Common cost: A cost which is incurred simultaneously for a whole organization, where it cannot be allocated directly to any particular product. These may be fixed or variable (e.g. the farm's driveway).

External and Internal Costs

External costs are discussed more in Negative externalities

Economics has a long tradition of distinguishing those costs which are fully internalized by economic agents (internal or private costs) and those which are not (external or social costs). The difference comes from the way that economics views the series of interrelated markets. Agents (individuals, households, firms and governments) in these markets interact by buying and selling goods are services, as inputs to and outputs from production. A firm pays an individual for labor services performed and that individual pays the grocery store for the food purchased and the grocery store pays the utility for the electricity and heat it uses in the store. Through these market transactions, the cost of providing the good or service in each case is reflected in the price which one agent pays to another. As long as these prices reflect all costs, markets will provide the required, desirable, and economically efficient amount of the good or service in question.

The interaction of economic agents, the costs and benefits they convey or impose on one another are fully reflected in the prices which are charged. However, when the actions of one economic agent alter the environment of another economic agent, there is an externality. An action by which one consumers purchase changes the prices paid by another is dubbed a pecuniary externality and is not analyzed here further; rather it is the non-pecuniary externalities with which we are concerned. More formally, "an externality refers to a commodity bundle that is supplied by an economic agent to another economic agent in the absence of any related economic transaction between the agents" (Spulber, 1989). Note that this definition requires that there not be any transaction or negotiation between either of the two agents. The essential distinction which is made is harm committed between strangers which is an external cost and harm committed between parties in an economic transaction which is an internal cost. A factory which emits smoke forcing nearby residents to clean their clothes, cars and windows more often, and using real resources to do so, is generating an externality or, if we return to our example above, the grocery store is generating an externality if it generates a lot of garbage in the surrounding area, forcing nearby residents to spend time and money cleaning their yards and street.

There are alternative solutions proposed for the mitigation of these externalities. One is to use pricing to internalize the externalities; that is, including the cost which the externalities impose in the price of the product/service which generate them. If in fact the store charged its customers a fee and this fee was used to pay for the cleanup we can say the externality of ‘unsightly garbage’ has been internalized. Closer to our research focus, an automobile user inflicts a pollution externality on others when the car emits smoke and noxious gases from its tailpipe, or a jet aircraft generates a noise externality as it flies its landing approach over communities near the airport. However, without property rights to the commodities of clean air or quiet, it is difficult to imagine the formation of markets. The individual demand for commodities is not clearly defined unless commodities are owned and have transferable property rights. It is generally argued that property rights will arise when it is economic for those affected by externalities to internalize the externalities. These two issues are important elements to this research since the implicit assumption is that pricing any of the externalities is desirable. Secondly, we assume that the property rights for clean air, safety and quiet rest with the community not auto, rail and air users. Finally, we are assuming that pricing, meaning the exchange of property rights, is possible. These issues are considered in greater detail in Chapter 3 where the broad range of estimates for the costs of the externalities are considered.

Other terms

• Sunk costs: These are costs that were incurred in the past. Sunk costs are irrelevant for decisions, because they cannot be changed.
• Indivisible costs: Do not vary continuously with different levels of output or must expenditures, but be made in discrete "lumps". Indivisible costs are usually variable for larger but not for smaller changes in output
• Escapable costs (or Avoidable costs): A cost which can be avoided by curtailing production. There are both escapable fixed costs and escapable variable costs. The escapability of costs depends on the time horizon and indivisibility of the costs, and on the opportunity costs of assets in question.

Time Horizon

Once having established the cost function it must be developed in a way which makes it amenable to decision-making. First, it is important to consider the length of the planning horizon and how many degrees of freedom we have. For example, a trucking firm facing a new rail subsidy policy will operate on different variables in the short run or a period in which it cannot adjust all of its decision variables than it would over the long run, the period over which it can adjust everything.

Long run costs, using the standard economic definition, are all variable; there are no fixed costs. However, in the short run, the ability to vary costs in response to changing output levels and mixes differs among the various modes of transportation. Since some inputs are fixed, short run average cost is likely to continue to fall as more output is produced until full capacity utilization is reached. Another potential source of cost economies in transportation are economies of traffic density; unit cost per passenger-kilometer decreases as traffic flows increase over a fixed network. Density economies are a result of using a network more efficiently. The potential for density economies will depend upon the configuration of the network. Carriers in some modes, such as air, have reorganized their network, in part, to realize these economies.

In the long run, additional investment is needed to increase capacity and/or other fixed inputs. The long run average cost curve, however, is formed by the envelope of the short run average cost curves. For some industries, the long run average cost often decreases over a broad range of output as firm size (both output and capacity) expands. This is called economies of scale. The presence of economies at the relevant range of firm size means that the larger the size of the firm, the lower the per-unit cost of output. These economies of scale may potentially take a variety of forms in transportation services and may be thought to vary significantly according to the mode of transportation involved.

Time horizon in economic theory

• Short run: the period of time in which the input of one or more productive agents is fixed
• Long run: the period of time in which all inputs are variable

actual length of the time horizon to use depends on

• the type of decision: when do the costs and benefits occur ?
• the expected life time of assets involved
• the time horizon for major transportation projects tends to be lengthy relative to that in other industries

The relationship between short and long run costs is explained by the envelope theorem. That is, the short run cost functions represent the behavior of costs when at least one factor input is fixed. If one were to develop cost functions for each level of the fixed factor the envelope or lower bound of these costs would form the long run cost function. Thus, the long run cost is constructed from information on the short run cost curves. The firm in its decision-making wishes to first minimize costs for a given output given its plant size and then minimize costs over plant sizes.

In the diagram below the relationship between average and marginal costs for four different firm sizes is illustrated. Note that this set of cost curves was generated from a non-homogeneous production function. You will note that the long run average cost function (LAC) is U-shaped thereby exhibiting all dimensions of scale economies.

Mathematically

$C\left(Q\right)\equiv C_{s}\left(Q,K\left(Q\right)\right)$

${\frac {\partial C\left(Q\right)}{\partial Q}}={\frac {\partial C_{s}\left(Q,K\left(Q\right)\right)}{\partial Q}}+{\frac {\partial C_{s}\left(Q,K\left(Q\right)\right)}{\partial K}}\bullet {\frac {\partial K\left(Q\right)}{\partial Q}}$

where: ${\frac {\partial C_{s}\left(Q,K\left(Q\right)\right)}{\partial K}}=0$ provides the optimal plant size.

Indicators of Aggregate Cost Behavior

Scale economies is the behavior of costs when the AMOUNT of an output increases while scope economies refers to the changes in costs when the NUMBER of outputs increases.

Economies of Scale

Economies of scale refer to a long run average cost curve which slopes down as the size of the transport firm increases. The presence of economies of scale means that as the size of the transport firm gets larger, the average or unit cost gets smaller. Since most industries have variable returns to scale cost characteristics, whether or not a particular firm enjoys increasing, constant or decreasing returns to scale depends on the overall market size and the organization of the industry.

The presence or absence of scale economies is important for the industrial structure of the mode. If there were significant scale economies, it would imply fewer larger carriers would be more efficient and this, under competitive market circumstances, would naturally evolve over time. Scale economies are important for pricing purposes since the greater are the scale economies, the more do average and marginal costs deviate. It would, therefore, be impossible to avoid a deficit from long run marginal [social] cost pricing.

Another note of terminology should be mentioned. Economics of scale is a cost concept, returns to scale is a related idea but refers to production, and the quantity of inputs needed. If we double all inputs, and more than double outputs, we have increasing returns to scale. If we have less than twice the number of outputs, we have decreasing returns to scale. If we get exactly twice the output, then there are constant returns to scale. In this study, since we are referring to costs, we use economies of scale. The presence of economies of scale does not imply the presence of returns to scale.

Scale measures long-run (fully adjusted) relationship between average cost and output. Since a firm can change its size (network and capacity) in the long run, Economies of Scale (EoS) measures the relationship between average cost and firm size. EoS can be measured from an estimated aggregate cost function by computing the elasticity of total cost with respect to output and firm size (network size for the case of a transport firm).

Returns to Scale (Output Measure)

Increasing Returns to Scale (RtS)

$f(tx_{1},tx_{2})>tf(x_{1},x_{2})$

Decreasing RtS

$f(tx_{1},tx_{2})<tf(x_{1},x_{2})$

Economies of Scale (Cost Measure)

Economies of scale (EoS) represent the behavior of costs with a change in output when all factors are allowed to vary. Scale economies is clearly a long run concept. The production function equivalent is returns to scale. If cost increase less than proportionately with output, the cost function is said to exhibit economies of scale, if costs and output increase in the same proportion, there are said to be 'constant returns to scale' and if costs increase more than proportionately with output, there are diseconomies of scale.

• if cost elasticity < 1, or $LRMC<LRAC$ -> increasing EoS
• if cost elasticity = 1, or $LRMC=LRAC$ -> constant EoS
• if cost elasticity > 1, or $LRMC>LRAC$ -> decreasing EoS

Economies of Density

There has been some confusion in the literature between economies of scale and economies of density. These two distinct concepts have been erroneously used interchangeably in a number of studies where the purpose was to determine whether or not a particular mode of transportation (the railway mode has been the subject of considerable attention) is characterized by increasing economies or diseconomies of scale. There is a distinction between density and scale economies. Density economies are said to exist when a one percent increase in all outputs, holding network size, production technology, and input prices constant, increase the firm’s cost by less than one percent. In contrast, scale economies exist when a one percent increase in output and size of network increases the cost by less than one percent, with production technology and input prices held constant.

Economies of density, although they have a different basis than scale economies, can also contribute to the shape of the modal industry structure. It can affect the way a carrier will organize the delivery of its service spatially. The presence of density economies can affect the introduction of efficient pricing in the short term, but generally not over the long term since at some point density economies will be exhausted. This, however, will depend upon the size of the market. In the air market, for example, deregulation has allowed carriers to respond to market forces and obtain the available density economies to varying degrees.

Returns to Density similar to returns to a capacity utilization when capacity is fixed in the short run. Since the plant size (network size for the case of transportation firms) is largely fixed in the short run, RTD measures the behavior of cost when increasing traffic level (output) given the plant size (network size). It is measured by the cost elasticity with respect to output.

• if cost elasticity < 1, or $SRMC<SRAC$ -> increasing EoD
• if cost elasticity = 1, or $SRMC=SRAC$ -> constant EoD
• if cost elasticity > 1, or $SRMC>SRAC$ -> decreasing EoD

Because of the presence of high fixed costs and cost of operating terminals (airports, stations, depots, etc), most transportation firms have increasing RTD.

Economies of Capacity Utilization

A subtle distinction exists between economies of density, which is a spatial concept, and economies of capacity utilization, which may be aspatial. As a fixed capacity is used more intensively, the fixed cost can be spread over more units or output, and we have declining average cost, economies of scale. However, as the capacity is approached, costs may rise as delays occur. This gives a u-shaped cost curve.

While economies of scale refer to declining average costs, for whatever reason, when output increases; and economies of density refer to declining costs when output increases and the network mileage is held constant; economies of capacity utilization refers to declining costs as the percentage of capacity which is used increases, where capacity may be spatial or aspatial.

While density refers to how much space is occupied, capacity refers to how much a capacitated server (e.g. a bottleneck, the number of seats on a plane) is occupied, and may incorporate economies of density if the link is capacitated, such as a congesting roadway. However if a link has unlimited (or virtually unlimited) capacity, such as intercity passenger trains on a dedicated right-of-way at low levels of traffic, then economy of density is a more appropriate concept. Another way of viewing the difference is that economies of density refers to linear miles, while economies of utilization refer to lane miles.

Economies of Scope

Economies of Scope

Typically, the transport firm produces a large number of conceptually distinct products from a common production facility. In addition, the products of most transportation carriers are differentiated by time, space and quality. Because a number of distinct non-homogeneous outputs are being produced from a common production facility, joint and common costs arise. The presence of joint and common costs give rise to economies of scope. There has been some confusion in the multi-product literature among the concepts of sub-additivity of the cost function, trans-ray convexity, inter-product complementarity and economies of scope. Sub additivity is the most general concept and refers to a cost function which exhibits the characteristic that it is less costly to produce different amounts of any number of goods in one plant or firm than to sub divide the products or service in any proportion among two or more plants. Trans-ray convexity is a somewhat narrower concept. It refers to a cost function which exhibits the characteristic that for any given set of output vectors, the costs of producing a weighted average of the given output vectors is no greater than the weighted average of producing them on a stand alone basis. Economies of scope refers to the cost characteristic that a single firm multi-product technology is less costly than a single product multi-firm technology. It, therefore, is addressing the issue of the cost of adding another product to the product line. Inter-product complementarity is a weak test of scope economies. It refers to the effect on the marginal cost of one product when the output of some other product changes. It, therefore, is changing the amount of output of two or more products and not the number of products. Whether scope economies exist and the extent to which they exist depend upon both the number of products and the level of each output. There have not been definitive empirical estimates of economies of scope for transportation modes which are based on reliable data and undertaken in a theoretically consistently fashion.

Thought Question: Most firms produce multiple products. Why do multiple product firms exist ?

It must be cheaper to have one firm to produce multiple products than have separate firms produce each type of product.

Economies of scope arise from shared or jointly utilised inputs, e.g., imperfectly divisible plant which if used to produce only one product would have excess capacity (freight and passenger services using same airplane, forward-back haul production using a truck or rail car, etc.).

This can be represented graphically as in the diagram on the right. In production space an isoquant would link two outputs and would have the interpretation of an isoinput line, that is, it would be the combination of outputs which are possible with a given amount of inputs. If there were economies of scope, the line would be concave to the origin, if there were economies of specialization it would be convex and if there were no scope economies it would be a straight line at 45 degrees.

Let $q=(q_{1},...,q_{n})$, $n$ = number of different outputs.

Economies of scope exists if

$c(q_{1})+...+c(q_{n})>c(q_{1},...,q_{n}).$

That is, it is cheaper to have one firm produce all outputs than to have n separate firms produce each output $q_{i}$, where $c(q)$ is the cost for a firm to produce output $q$.

Scope economies are a weak form of 'transray convexity' and are said to exist if it is cheaper to produce two products in the same firm rather than have them produced by two different firms. Economies of scope are generally assessed by examining the cross-partial derivative between two outputs, how does the marginal cost of output one change when output two is added to the production process.

Changes in Cost

Costs can change for any number of different reasons. It is important that one is able to identify the source of any cost increase or decreases over time and with changes in the amount and composition of output. The sources of cost fluctuations include:

• density and capacity utilization; movements along the short run cost function
• scale economies; movements along the long run cost function
• scope economies; shifts of the marginal cost function for one good with changes in product mix
• technical change which may alter the level and shape of the cost function

Characterizing Transportation Costs

All modes of transport experience:

• economies of vehicle size up to a point
• increasing returns in provision of way and track capacity
• economies of longer distance travelled
• rapidly rising average cost with increased speed;
• exponentially increasing energy consumption with speed
• difficultly in identifying the costs associated with particular traffic because of indivisibilities in production and heterogeneity of output
• declining unit costs over a range of output because of indivisibilities,
  • e.g. the backhaul problem, increase in traffic on the backhaul will reduce the average costs of the round trip operation
  • indivisibilities in production give rise to "kinked" average cost curves and discontinuous marginal costs

Costing

Costing is the method or process of ascertaining the relationship between costs and outputs in a way which is useful for making decisions (managerial, strategic, regulatory policy etc.). There are numerous examples where detailed cost information is necessary for carriers' management decisions and government's regulatory decisions. Also there are many carrier and government decisions requiring information about the behaviour of aggregate costs of a firm.

Carrier Management Decisions

Requiring disaggregate cost info:

• rates and rate structure decisions;
  • rate setting
  • shipper-carrier negotiations
• financial viability of specific services; e.g.,
  • rail passenger operations,
  • rail branch lines
• decision to launch a specific service
• application of subsidies
• compensation for running rights;
  • passenger trains
  • leased right of way

Requiring aggregate cost info:

• carrier network plan
• plan for mergers and acquisitions
• strategic plan
• major investment decisions

Policy Decisions

Requiring disaggregate cost info:

• enforcing pricing regulation
• decisions on public subsidies
• branchline abandonment decision - "short-line" sales
• user charges for government-owned infrastructure

Requiring aggregate cost info:

• decision on price and entry regulation;
  • natural monopoly question - scale and density economies
  • effect of regulation on efficiency;
    • allocative efficiency
    • X-efficiency
• approval of mergers and acquisition - scale and density economies
• decisions on transport infrastructure investment
• licensing of competitive services

Aggregate Cost Analysis

Econometric cost functions are estimated to study the behaviour of aggregate costs in relation to the aggregate output level (economies of scale) and output mix (economies of scope). The aggregate cost function also allows one to estimate the changes in productive efficiency over time. This allows inference about the effect of regulation on productivity of an industry

Which Costs

Economic theory suggests that costs are a function of at least factor prices and outputs. In practice, calculating costs, prices, or outputs can be tricky. For example, how should capital costs be determined ?

Capital costs may occur over one year but it is likely to be used over a long period of time. So we should use the opportunity costs which includes depreciation and interest costs. The capital stock of a firm will vary year to year.

Accountants tend to use historical costs which do not account for inflation. The point is that in the real world get all sorts of complications.

Prices and Outputs

For prices and outputs, a firm may use many inputs and provide many different outputs. Transportation outputs are produced over a spatial network. An appropriate definition of outputs is the movement of a commodity/passenger from an origin to a destination - a commodity/passenger trip. A trip from A to B is different from a trip from C to D (or B to A) even if the same distance. Ideally, a transport cost model should account for this multiproduct nature. But cannot specify thousands of outputs -some aggregate is necessary. Often. lack of data requires aggregation to a single output measure like ton-kilometres or passenger-kilometres.

Attribute Variables

To account for the multidimensional heterogeneous nature of outputs, one can use attribute variables such as average length of haul or average stage length. They will vary by firms. Operating characteristics such as average shipment size, average load factor, etc., also affect costs. For example, if plane or truck is not full, there is unused capacity; adding a commodity trip may incur little marginal cost; longer distances can lower AC by spreading terminal costs or takeoff fuel costs.

Estimation

Cost function Estimation requires decisions on:

• short run vs. long run cost function
  • short run cost functions from time series data;
  • long run cost functions from cross-section data;
• variable vs. total cost function;
  • variable cost functions are estimated by fixing some inputs such as physical plants (rail roadbed and track; aircraft fleet, etc)
• the choice of functional form
• the choice of output measure;
  • single vs. multiple output measures
  • revenue output vs. available output
• the choice of the level of aggregation of cost accounts
• the choice of attribute variables to account for heterogeneous nature of outputs being produced over time or across different firms in the sample data.

Difficulties with Costing

• multi-dimensionality and heterogeneous nature of outputs
• indivisibilities in production
• costs may not occur at the same time as the outputs being produced. eg. capital costs may over one year but it is likely to be used over several years, and some expenses occur some time after the increases in outputs (expenses occur less frequently than changes in (train) trips), etc
• ambiguity in cost standards
• difficulty of relating past to future
  • input price changes
  • changes in production technology
  • changes in operating conditions

Disaggregate Costing

Disaggregate costing can be used to estimate the variable cost of a block of traffic, or traffic on a particular line,etc. it is useful for setting rates, investment decisions, subsidy determinations, etc. by companies themselves or government

Deductive (economic) vs inductive (engineering) approaches are used in transportation modeling, and analysis. The deductive approach uses modeling and prior relationships to specify a functional relationship which is then examined statistically. An inductive approach is based on a detailed understanding of physical processes.

Inductive Approaches

• Use of Engineering Relationships

Economic Approaches

• Average Cost Calculation using Accounting Info
• Statistical Costing

Engineering Costing

Engineering costing focuses on the amount of each input required to produce a unit of output, or the technical coefficients of production. combining such coefficients with the costs of the inputs yields the cost function for the particular output.

There are two approaches to engineering costing:

• to derive the technical coefficients from physical laws or precise engineering relationships.
• to empirically establish the technical relationship by controlled experiment.

• advantage
  • Accuracy ? Precision?
• shortcomings:
  • data- and time-intensive costly
  • nonstochastic
  • must have well defined production processes

Accounting Costing

• compiles the cost accounts categories relevant to the output or service in question, and use that information to estimate the costs associated with a specific movement.
• advantages:
  • relatively cheap
  • convenient
• shortcomings:
  • data/information must exist
  • the recorded values of assets may not be a reliable indicator of the actual opportunity costs of those assets
  • the cost accounts may not distinguish fixed vs. variable costs Y over estimation of the marginal cost.
  • the accounts are classified by the types of expenses, not by output type, it is difficult to uncover the true relations between cost and outputs
  • the aggregation in the accounts may prevent identifying the costs which can be related to the production of particular outputs

Statistical Costing

Statistical costing employes statistical techniques (usually multiple regression analysis) to infer cost-output relationships from a sample of actual operating experiences. It makes use of accounting information.

Basic steps in statistical costing are:

(1) Decompose and identify the intermediate work units associated with the specific traffic. For example, costing 500 tons of coal from point a to b, intermediate work units may consist of line haul, switching, terminal activities, administration, etc. Explanatory variables for these activities would include ton-miles, car-miles, yard-switching miles, train-hours, gallons of fuel, etc.

(2) Establish relationship between factor inputs and the intermediate process. This can be done by direct assignment of an expense category to the work unit, if causal relation is clear. Often, expenses are common to several types of traffic, so estimate statistical relationship with regression analysis.

For example, regression of track and roadway maintenance (TRM)

$TRM=f({\text{ton-miles, yard-switching minutes, train switching minutes, road miles}})$

(3) Apply the marginal/unit costs of the intermediate work units estimated in step (2) to the work units identified in step (1).

(4) Sum all expenses in step (3) to calculate the total avoidable cost of a block of traffic.

Evidence on Carrier Costs

How do the long run concepts of economies of scale and economies of scope and the short run concepts of economies of density and economies of capacity utilization influence costs? Why are they important to our discussion of transport infrastructure pricing? These questions will be addressed in the following section.

Air Carriers

A considerable number of studies, Douglas and Miller (1974) , Keeler (1974) , Caves, Christensen and Tretheway (1984) , Caves, Christensen, Tretheway and Windle (1985), McShan and Windle (1989), and Gillen, Oum, and Tretheway (1985, 1990), have been directed at determining the functional relationship between total per-unit operating costs and firm size in airlines. All studies have shown that economies to scale are roughly constant; thus, size does not generate lower per-unit costs. However, generally, the measures of economies of density illustrate that unit cost would decrease for all carriers if they carried more traffic within their given network. In other words, the industry experienced increasing returns to density. The results also indicated that the unexploited economies of density are larger for low density carriers. Caves, Christensen, and Tretheway (1984) have shown that it is important when measuring costs to include a network size variable in the cost function, along with output, which would allow for the distinction between economies of scale and economies of density. McShan and Windle (1989) utilize the same data set as that used by Caves et al., and explicitly account for the hub and spoke configuration that has developed in the US since deregulation in 1978. They estimate a long run cost function which employs all the variables included in Caves et. al., and found economies to density of about 1.35. The hubbing variable indicates that, ceteris paribus, a carrier with 1% more of its traffic handled at hub airports expects to enjoy 0.11% lower cost than other similar carriers.

Intercity Buses

Gillen and Oum (1984) found that the hypothesis of no economies of scale can be rejected for the intercity bus industry in Canada; there are diseconomies of scale at the mean of the sample (0.91). Large firms were found to exhibit strong diseconomies of scale, and small and medium sized firms exhibit slight departures from constant returns. No cost complementarities are found to exist between the three outputs, namely, number of scheduled passengers, revenue vehicle miles of charter, tour and contract services, and real revenue from freight. These results, however, may be biased since no network measure was included in the estimating equations. The scale economy measure will, therefore, contain some of the influence of available density economies.

Since deregulation of the intercity bus industries in the US and the UK., the number of firms has been significantly reduced. In the absence of scale economies, the forces leading to this industry structure would include density economies. We have, for example, observed route reorganization to approximate hub-and-spoke systems and the use of smaller feeder buses on some rural routes. The industry reorganization is similar to what occurred in the airline industry. The consolidation of firms was driven by density and not scale economies. One significant difference between these two industries, however, is airline demand has been growing while intercity bus demand is declining.

Railway Services

The structure of railway costs is generally characterized by high fixed costs and low variable costs per unit of output. The essential production facilities in the railway industry exhibit a significant degree of indivisibility. As with other modes, the production of railway services give rise to economies of scope over some output ranges. For example, track and terminals used to produce freight services are also used to produce passenger services.

Caves, Christensen and Tretheway (1980) have found that the US railway industry is characterized by no economies of scale over the relevant range of outputs. However, their sample does not include relatively small railroads, firms with less than 500 miles of track. Griliches (1972) and Charney, Sidhu and Due (1977) have found economies scale for such small US railroads. Friedlaender and Spady (1981) suggested that there may be very small economies of scale with respect to firm size. Keeler (1974), Harris (1977), Friedlaender and Spady (1981) and Levin (1981) have all shown that there are large economies of traffic density in the US railroad industry. They show that, allowing all factors of production except route mileage to vary, a railway producing 10 million revenue ton-miles per mile of road, for example, will have substantially lower average costs than will a railway producing only 5 million revenue ton-miles per mile of road. Harris (1977) estimated that approximately one-third of density economies were due to declining average capital costs, and two-thirds due to declining fixed operating costs, such as maintenance, and administration. Friedlaender and Spady (1981) estimate a short run cost function with five variable inputs, one quasi-fixed factor (structures) and two outputs which take the form of hedonic functions, accounting for factors such as low density route miles and traffic mixes. The study found no economies of scale. Caves, Christensen, Tretheway and Windle (1985) have examined economies of scale and density in the US railroads. Their basic result demonstrates that there are substantial economies of density in the US railway operations.

Evidence on Infrastructure Costs

As early as 1962, Mohring and Harwitz demonstrated that the financial viability of an infrastructure facility, under optimal pricing and investment, will depend largely upon the characteristics of its cost function. To quote Winston (1991): “ If capacity and durability costs are jointly characterized by constant returns to scale, then the facility’s revenue from marginal cost pricing will fully cover its capital and operating costs. If costs are characterized by increasing returns to scale, then marginal cost pricing will not cover costs; conversely, if costs are characterized by decreasing returns to scale, marginal cost pricing will provide excess revenue.”

The objective of this section is to provide a summary of the theoretical and empirical literature on the cost characteristics of modal infrastructure. The discussion will deal with the following types of infrastructure: airports, highways, and railways.

In developing a set of socially efficient prices for modes of intercity transport, it is not just the carrier’s cost structure which is important. Airports, roadways and harbors all represent public capital which is used by the carriers in the different modes to produce and deliver their modal services. This capital must also be priced in an efficient way to achieve the economic welfare gains available from economically efficient pricing. As with the carriers, the ability to apply first best pricing principles to infrastructure and still satisfy cost recovery constraints will depend upon the cost characteristics of building and maintaining the infrastructure.

As with carriers, the cost characteristics for infrastructure providers include scale economies, scope economies, density economies and utilization economies. Scale economies refer to the size of a facility; for example, is it cheaper to build three runways than it is to provide two runways? If so, there are economies of scale in the provision of runways. Scope economies encompass similar concepts as with carriers. Small, Winston and Evans (1989) refer to scope economies in highways when both capacity and durability are supplied. Capacity refers to the number of lanes while durability refers to the ability to carry heavier vehicles. A similar concept would apply to airports: small and large aircraft, VFR and IFR traffic, and to harbors: large ships and small ships. Although rail infrastructure is currently supplied by the same firms operating the trains, there have been moves to separate infrastructure and carrier services. This separation will mean the track and terminals will have to be priced separately from carrier services.

Density economies should also, in principle, be evident in the provision of infrastructure. It is, for example, possible to expand outputs and all inputs for highways while holding the size of the network fixed.

Utilization economies refer to the short run cost function. They describe how quickly average and marginal costs will fall as capacity utilization approaches capacity. Although not of direct interest, they are important to consider in any cost estimation since failure to consider capacity utilization can bias upward the measures of both long run average and marginal costs.

Airports

Economists have typically assumed that capacity expansion is divisible. Morrison (1983), in his analysis of the optimal pricing and investment in airport runways, has shown that airport capacity construction is characterized by no economies of scale, and, therefore, under perfect divisibility of capacity expansion, the revenue from tolls will be exactly equal to the capital cost of capacity investment (Mohring and Harwitz, 1962). Morrison’s results, however, were based on a sample of 22 of the busiest airports in the US and did not include any small airports. In the literature, there is no empirical evidence on the cost characteristics of capacity construction of new small airports or capacity expansion of existing small airports (e.g. one runway).

Highways

In general, highways produce two outputs: traffic volume which requires capacity in terms of the number of lanes, and standard axle loading which require durability in terms of the thickness of the pavement. Prior to determining economies of scale in this multi-product case, the measure of economies of scale for each output, or the product specific economies of scale, must be examined. Small, Winston, and Evans (1989) reported the existence of significant economies of scale associated with the durability output of roads, the ability to handle axle loads. This is because the pavement’s ability to sustain traffic increases proportionally more than its thickness. They also found evidence that there are slight economies of scale in the provision of road capacity; i.e. the capacity to handle traffic volume. However, they reported diseconomies of scope from the joint production of durability and capacity because as the road is made wider to accommodate more traffic, the cost of any additional thickness rises since all the lanes must be built to the same standard of thickness. They conclude that these three factors together result in highway production having approximately constant returns to scale. In other words, the output-specific scale economies are offset by the diseconomies of scope in producing them jointly.

Railways

An important difference between rail and other modes of transportation is that most railroads provide the infrastructure themselves and the pricing is undertaken jointly for carrier services and infrastructure. However, in a few cases, ownership and/or management of the trackage has been separated from carriers. Sweden is a good example but even in the US there have been joint running rights on tracks. This creates a situation whereby one firm may be responsible for the provision of trackage and another for carrier services. It is, therefore, legitimate to ask if there are any scale economies in the provision of railway infrastructure. There are no empirical estimates but it may be possible to use some of the Small, Winston and Evans (1988) work for roads to shed some light on the issue.

Small et al. argue road infrastructure produces two outputs, durability and capacity. The former refers to the thickness of roads and the latter to their width. They found economies with respect to durability, but this is less likely to occur with a rail line since there would be a relatively broad range of rail car axle loading for a given level of durability of rail, ballast and ties. Thus, there may be some minor economies. The authors found diseconomies of scope from the joint production of durability and capacity for highways. These diseconomies are less likely to be evident in rail due to the broad range of durability noted above and the ability to restrict usage to specific tracks. On balance, it may be there are generally constant or minor economies in the provision of rail line infrastructure. The output specific scale economies seem to be minor as do the diseconomies of producing them jointly.

Factors affecting Transportation Costs

Transportation costs seem to be rising, There are many factors which might explain this. These are listed below. This list is no doubt incomplete, but may serve as a point of discussion.

1. Standards
   1. Standards have risen - Society now demands safety, features, environmental protection, access for the disabled, and quality that drive up the cost. Engineering design is often 20% of project costs. Does the firetruck really need to do a 360 degree turn on the cul-de-sac, or can it back out?
   2. Smith's Man of System - The man of system . . . is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess-board. He does not consider that the pieces upon the chess-board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might chuse to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder. -- Adam Smith, The Theory of Moral Sentiments, 1759
   3. Gold-plating - Adding needless or useless features to projects. The costs of gold plating are several. Money spent on project X cannot be spent on project Y. This is the monetary opportunity cost of misallocation. Land devoted to project X cannot be devoted to project Y. More land also means greater distances to traverse. This is a spatial opportunity cost. There is a tension between the risk of gold plating (focus on benefits to the exclusion of cost) and of corner cutting (focusing on costs to the exclusion of benefits). But there is available to us a balance, building something which maximizes the difference between benefits and costs, not just looking at benefits or costs. Insufficient attention is placed on the trade-off, too much on the ends by advocates of one side or the other.
   4. Design for forecast.
   5. The State Aid system and associated standards - Funds are collected at the state and federal levels for transportation and then a portion of that money is transferred back to local governments for transportation. Along with the money comes requirements that dictate how that money is to be used. These include engineering requirements for things such as lane width, degree of road curvature and design speed and planning requirements for things like maintaining a hierarchical road network.
   6. Doing construction on facilities still in operation. - Aside from the rare bridge, it is unnecessary to keep facilities opening and operating while doing construction. This reduces construction space, reducing time, increases set-up/break-down costs, and otherwise adds to total costs. Construction is much faster (and thus cheaper) if rebuilding could be done on a closed facility. See the w: Tube Lines as the classic example of the high cost of doing construction only at night and weekends, but keeping the line in operation. The system as a whole must be reliable, meaning I can get from here to there, but that does not mean every segment must be open 24/7/365. One reason the reconstruction of the I-35W bridge was so fast as that they contractors did not need to worry about existing traffic, (and it was design/build).
   7. Environmental Impact Statements (Reports) lead to "lock-in"
   8. Open government/costs of democracy - The planning process is required by law to bring in as many stakeholders as possible. This has (potentially) led to transportation investment being sought and justified for non-transportation concerns. Transportation investment is now used for social, moral and economic goals that are not directly related to mobility.
   9. Climate change adaptation is increasing the costs of projects.
2. Scale economies
   1. There are in-sufficient economies of scale - When everything is bespoke, there is no opportunity for standardization and economies of scale. While many rail against cookie-cutter design, it is only with cookie-cutters that we get lots of cookies.
   2. Thin markets - There is no online department store for public works. I cannot go online and buy a transit bus or an interchange. The internet has not driven down prices in this field the way it has in so many others. As a result a few vendors can collude or orchestrate higher prices than would be faced in a more competitive market.
   3. Peaking - Transportation agencies attempt to provide high levels of peak capacity to accommodate the demand that results from un-priced roads and highways. This is very costly capacity to provide. If tolls were charged that reflected true costs people would drive less, especially during peak hours. It would therefore cost much less to provide the economically optimal amount of peak system capacity.
3. Change of scope
   1. Projects are scoped wrong - We have investments that don't match actual demands. And this is not just for megaprojects. We have big buses serving few passengers. We have overgrown highways. We have a fear of building too small and having congestion or crowding so we build too big.
   2. Project creep - Side-payments in project development: noise walls hither and thither, etc. Side-payments are a required part of the politics of getting something built.
   3. "Starchitecture",
   4. Fragmented governance leads to large and meandering projects rather than centralized projects. Politicians have to "share the wealth" of projects. This is perhaps a cause of "project creep."
4. Principal-agent problems
   1. Other people's money - Public works agencies are spending Other People's Money, and so are less motivated to get value for dollar than an individual consumer on their own. This principal-agent problem prevails in lots of organizations, but especially so in public works where the bias is not to have a failure. There was an old saying in business, no one ever got fired for buying IBM. The same holds in public works, where rocking the boat with new or innovative technologies is not sufficiently rewarded.
   2. Benefits are concentrated, costs are diffuse - As a result, the known beneficiaries lobby hard for projects, but not just to build it, but to build it in a way that is expensive. Costs are diffuse, it is seldom worth the taxpayer's time to oppose a project just because of its costs, which are spread among millions of other taxpayers. See: w:The Logic of Collective Action.
   3. Decision-makers are remote - Remote actors cannot have precise information about local conditions, and in the absence of a free market in transportation (there is generally one buyer, who is generally a government agency), prices are not clear. As a result these remote actors misallocate because they are misinformed. This notion derives from the w: Economic calculation problem See w:The Fatal Conceit.
   4. Benefit cost analysis is only as good as the integrity of the data and the analysts.
   5. B/C analysis is not used to affect project outcomes.
   6. Planners and engineers are paid as percentage of total project cost.
   7. Formula spending reduces the incentive or need to worry much about costs. This is obviously related to many of the other hypotheses already considered but I think deserves it's own number.
   8. Lack of user fee funding - projects funded out of user fees are more likely to be efficient, partly because the agencies or private parties receiving those fees know the fees are limited and partly because they want to spend them in ways that will generate more fees (which means in ways that benefit users enough that the users are willing to pay for them).
   9. Federal funds favor capital-heavy technologies and investments. - Federal funding programs create perverse incentives that lead to very costly capital projects. Almost any project looks good if somebody else is paying for most of it. For example every year billions of dollars are spent on passenger rail projects that would never be funded were it not for generous Federal grants. Just look at the high speed rail program or the FTA New Starts program. There are examples on the highway side too, such as bridges to nowhere and freeways in rural areas with little traffic. These Federal programs, no matter how well intentioned, tip the local decision making process in favor of expensive capital projects and discourage consideration of lower cost options and policy reforms.
   10. Public ownership - Most of the transportation system is owned, planned, and managed by public agencies. These entities have many objectives but efficiency and cost-effectiveness are rarely a high priority. The public sector does some things well but it doesn't usually do them very efficiently. As a result transportation revenues are not always efficiently converted to transportation user benefits.
   11. Multi-jurisdiction - Because transportation involves a large number of public agencies with overlapping or intertwined responsibilities planning is complex and inefficient. Projects end up with all the bells and whistles needed to satisfy the agencies and constituencies that could block a proposal. Local elected officials often load up regional plans with pet projects that do little to improve transportation system performance. There is a whole science to how public agencies bargain with each other and interact, unfortunately the results are rarely optimal from a cost-effectiveness perspective. The principal/agent problem is part of the reason for this, but only a part. In nearly every metropolitan area in the United States institutional structure results in transportation plans and policies that fall far short of the cost-effectiveness that could be achieved.
   12. Graft.
   13. Poor commissioning - Contracts determining who does what on a project are poorly written, and affect outsourced projects.
   14. Separation of design and build - Different firms are responsible for engineering and construction, creating high communication costs.
   15. Union work rules (not wages) that inhibit productivity gains through new technologies.
   16. Public-private partnerships trade additional up front costs for faster construction.
5. Project Duration
   1. Paralysis by analysis - The bureaucratic requirement to do analysis delays projects and adds costs
   2. Lack of upfront funds - Delays projects adds to ultimate costs.
   3. Lack of consensus - Political requirements for consensus add delays.
   4. Mismanagement and graft add to delays.
6. Other
   1. The highest demand areas for maintenance and new stock occur in places that are expensive.
   2. Envy - is a much bigger problem in public works than in personal life. - I pay taxes for those things, why does Jurisdiction X get an LRT when my neighborhood/district doesn’t? It’s a recipe for political hostages at budget time, as few political leaders have any reason to say "You know, the benefit cost on a project in my district just shows the project makes no sense." It’s leads to two problems: projects that make no sense to serve some notion of geo-political equity, and project creep because if Jurisdiction X’s light rail stations had public art and golden knobs and a fountain, then my district’s light rail should have those and more. Combined with the Other People’s Money problem, this type of envy is a recipe for project creep.
   3. Materials are scarcer (and thus more expensive).
   4. Stop/start investment.
   5. w:Ratchet effect - Interest groups are attracted to a particular public issue and pressure the legislative body to increase spending on that issue, but make it impossible to decrease spending on the issue.
   6. w:Baumol's cost disease - The rise of wages in jobs without productivity gains is caused by the necessity to compete for employees with jobs that did experience gains and hence can naturally pay higher salaries.
   7. Transit investment isn't realizing any productivity gains from labor. - Every dollar spent on public transportation yields 70% more jobs than a dollar spent on highways. This is used to bolster the argument that we should spend more on transit, but instead suggests we are much better at building roads than at building transit. As labor is a large proportion of total cost, transit investment has not realized productivity gains that have occurred in road building. This could be explained in part by lack of competition, low levels of total investment haven't brought new producers into the market, or a number of other reasons. I don't think the relatively high number of jobs per dollar spent necessarily means that transit investment is more virtuous. It may just be more inefficient. This is a problem with treating transport investment as industrial policy.
   8. Utility works are uncharged.
   9. Experience and Competence - The US has no experience with high-speed rail, so there is no domestic expertise.
   10. Ethos, training and prestige - Transportation engineering is more prestigious in other countries.
   11. Government power - Governments have more power to implement in other countries.
   12. Legal system - Legal systems are more amenable to infrastructure construction, including liability, bonds, and insurance.

Negative externalities

An externality is a cost or benefit incurred by a party's decision or purchase on another, who neither consents, nor is considered in the decision. One example of a negative externality we will consider is pollution

Introduction

There has been a long-standing interest in the issue of the social or external costs of transportation (see for instance: Keeler et al. 1975 , Fuller et al. 1983 , Mackenzie et al. 1992, INRETS 1993 , Miller and Moffet 1993 , IWW/INFRAS 1995 , IBI 1995 ). The passions surrounding social costs and transportation, in particular those related to the environment, have evoked far more shadow than light. At the center of this debate is the question of whether various modes of transportation are implicitly subsidized because they generate externalities, and to what extent this biases investment and usage decisions. On the one hand, exaggerations of environmental damages as well as environmental standards formulated without consideration of costs and benefits are used to stop new infrastructure. On the other hand, the real social costs are typically ignored in financing projects or charging for their use.

Associated with the interest in social and external cost has been a continual definition and re-definition of externalities in transportation systems. Verhoef (1994) states “An external effect exists when an actor’s (the receptor’s) utility (or profit) function contains a real variable whose actual value depends on the behavior of another actor (the supplier) who does not take these effects of his behavior into account in this decision making process.” This definition eliminates pecuniary externalities (for instance, an increase in consumer surplus), and does not include criminal activities or altruism as producers of external benefits or costs. Rothengatter (1994) presents a similar definition: “an externality is a relevant cost or benefit that individuals fail to consider when making rational decisions.” Verhoef (1994) divides external cost into social, ecological, and intra-sectoral categories, which are caused by vehicles (in-motion or non-in-motion) and infrastructure. To the externalities we consider (noise, congestion, crashes, pollution), he adds the use of space (e.g. parking) and the use of matter and energy (e.g. the production and disposal of vehicles and facilities). Button (1994) classes externalities spatially, considering them to be local (noise, lead, pollution), transboundary (acid rain, oil spills), and global (greenhouse gases, ozone depletion). Gwilliam and Geerlings (1994) combines Verhoef’s and Button’s schemes, looking at a Global, Local, Quality of Life (Social), and Resource Utilization (air, land, water, space, materials) classification.

Rothengatter (1994) views externalities as occurring at three levels: individual, partial market, total market, and argues that only the total market level is relevant for checking the need of public interventions. This excludes pecuniary effects (consumer and producer surplus), activities concerning risk management, activities concerning transaction costs. Externalities are thus public goods and effects that cannot be internalized by private arrangements.

Rietveld (1994) identifies temporary effects and non-temporary effects occurring at the demand side and supply side. Maggi (1994) divides the world by mode (road and rail) and medium (air, water, land) and considers noise, crashes, and community and ecosystem severance. Though not mentioned among the effects above, to all of this might be added the heat output of transportation. This leads to the “urban heat island” effect -- with its own inestimable damage rate and difficulty of prevention.

Coase (1992) argues that the problem is that of actions of firms (and individuals) which have harmful effects on others. His theorem is restated from Stigler (1966) as “... under perfect competition, private and social costs will be equal.” This analysis extends and controverts the argument of Pigou (1920) , who argued that the creator of the externality should pay a tax or be liable. Coase suggests the problem is lack of property rights, and notes that the externality is caused by both parties, the polluter and the receiver of pollution. In this reciprocal relationship, there would be no noise pollution externality if no-one was around to hear. This theory echoes the Zen question “If a tree falls in the woods and no-one is around to hear, does it make a sound?”. Moreover, the allocation of property rights to either the polluter or pollutee results in a socially optimal level of production, because in theory the individuals or firms could merge and the external cost would become internal. However, this analysis assumes zero transaction costs. If the transaction costs exceed the gains from a rearrangement of activities to maximize production value, then the switch in behavior won’t be made.

There are several means for internalizing these external costs. Pigou identifies the imposition of taxes and transfers, Coase suggests assigning property rights, while our government most frequently uses regulation. To some extent all have been tried in various places and times. In dealing with air pollution, transferable pollution rights have been created for some pollutants. Fuel taxes are used in some countries to deter the amount of travel, with an added rationale being compensation for the air pollution created by cars. The US government establishes pollution and noise standards for vehicles, and requires noise walls be installed along highways in some areas. Therefore, a consensus definition might be, “Externalities are costs or benefits generated by a system (in this case transportation, including infrastructure and vehicle/carrier operations,) and borne in part or in whole by parties outside the system.”

Definitions

An externality is that situation in which the actions of one agent imposes a benefit or cost on another economic agent who is not party to a transaction.

Externalities are the difference between what parties to a transaction pay and what society pays

• A pecuniary externality, increases the price of a resource and therefore involves only transfers,
• A technical externality exhibits a real resource effect. A technical externality can be an external benefit (positive) or an external disbenefit (negative).

Examples

Negative externalities (external disbenefits) are air pollution, water pollution, noise, congestion.

Positive externalities (external benefits) include examples such as bees from apiary pollinating fruit trees and orchards supplying bees with nectar for honey.

Cause

The source of externalities is the poorly defined property rights for an asset which is scarce. For example, no one owns the environment and yet everyone does. Since no one has property rights to it, no one will use it efficiently and price it. Without prices people treat it as a free good and do not cost it in their decision making. Overfishing can be explained in the same way.

We want that amount of the externality which is only worth what it costs. Efficiency requires that we set the price of any asset >0 so the externality is internalized. If the price is set equal to the marginal social damages, we will get a socially efficient amount of the good or bad. Economic agents will voluntarily abate if the price is non-zero.

The Coase Theorem states that in the absence of transaction costs, all allocations of property are equally efficient, because interested parties will bargain privately to correct any externality. As a corollary, the theorem also implies that in the presence of transaction costs, government may minimize inefficiency by allocating property initially to the party assigning it the greatest utility.

Pareto Optimality

A change that can make at least one individual better off, without making any other individual worse off is called a Pareto improvement: an allocation of resources is Pareto efficient when no further Pareto improvements can be made.

Thought Question

What is the Optimal Amount of Externality?

(Is it zero? Why or why not?)

Damages vs. Protection

Social Costs: Damages vs. Protection

Social Costs: Supply and Demand

The tradeoff between benefits and costs is central to most economic analyses. Costs and benefits are both measurable and immeasurable, and a complete analysis must consider transaction and information costs as well as market costs. Individuals strive to maximize net benefits (benefits after considering costs), society might apply this to social costs as well. Reducing damages requires increasing protection (defense, abatement, or mitigation) to attenuate the damage. At some point, the cost of protection outweighs the benefit of reducing residual damages. This is illustrated in the figure. Whether this point is at zero damages (no damage is acceptable), zero protection (the damage is so insignificant as to be irrelevant), or somewhere in between is an empirical question. Total social costs are minimized where the marginal cost of additional damages equals the cost of additional protection. Whether the marginal costs of damage and of protection are fixed, rising or declining with output, and by how much will be another important empirical question.

The notion of damages and protection is compatible with the idea of supply and demand, as illustrated in the figure to the right. Here, the change in damages with output ($dD/dQ$) is the demand curve (the marginal willingness to pay to avoid damage), and the change in protection (attenuation) with output is the supply curve (marginal cost) and represented as ($dA/dQ$). Again, the slopes of the curves are speculative:

In the next Figure, area A represents the consumer surplus, or the benefit which the community receives from production, and is maximized by producing at qo (marginal cost of protection or attenuation equals the marginal cost of defense). The shaded area B represents production costs, and is the amount of social cost at the optimal level of production. Area C is non-satisfied demand, and does not result in any social costs so long as production remains at $q_{o}$.

Systems

Social Costs: Causes and Effects. Source:

Central to the definition and valuation of externalities is the definition of the system in question. The intercity transportation system is open, dynamic, and constantly changing. Some of the more permanent elements include airports, intercity highways , and railroad tracks within the state. The system also includes the vehicles using those tracks (roads, rails, or airways) at any given time. Other components are less clear cut - are the roads which access the airports, freeways, or train stations part of the system? The energy to propel vehicles is part of the system, but is the extraction of resources from the ground (e.g. oil wells) part of the system? DeLuchi (1991) analyzes them as part of his life-cycle analysis, but should we? Where in the energy production cycle does it enter the transportation system?

Any open system influences the world in many ways. Some influences are direct, some are indirect. The transportation system is no exception. Three examples may illustrate the point:

1. Cars on roads create noise—this we consider a direct effect.
2. Roads reduce the travel time between two places, which increases the amount of land development along the corridor—this is a less direct effect, not as immediate or obvious as the first. Other factors may intervene to cause or prevent this consequence.
3. The new land development along the corridor results in increased demand for public schools and libraries—this is clearly an indirect effect of transportation.

As can be seen almost immediately, there is no end to the number or extent of indirect effects. While recognizing that the economy is dynamic and interlinked in an enormous number of ways, we also recognize that it is almost impossible to quantify anything other than proximate, first order, direct effects of the transportation system. If the degree to which “cause” (transportation) and “effect” (negative externality) are correlated is sufficiently high, then we consider the effect direct; the lower the probability of effect following from cause, the less direct is the effect. The question of degree of correlation is fundamentally empirical.

On the other hand, this raises some problems. Automobiles burn fuel that causes pollution directly. Electric powered high speed rail uses energy from fuel burned in a remote power plant. If the electricity is fully priced, including social costs, then there is no problem in excluding the power plant. But, if the social costs of burning fuel in a power plant are not properly priced, then to ignore these costs would be biased. This is the problem of the first best and second best. The idea of the first best solution suggests that we optimize the system under question as if all other sectors were optimal. The second best solution recognizes that other systems are also suboptimal. Clearly, other systems are suboptimal to some extent or another. However, if we make our system suboptimal in response, we lessen the pressure to change the other systems. In so doing we effectively condemn all other solutions to being second best.

Button (1994) develops a model relating ultimate economic causes to negative externalities and their consequences as summarized in the following graphic. Users and suppliers do not take full account of environmental impacts, leading to excessive use of transport. Button argues that policy tools are best aimed at economic causes, but in reality measures are aimed at any of four stages. Here we are considering the middle stage, physical causes and symptoms, and are ignoring feedback effects.

Another view has the “externalities” as inputs to the production of transportation, along with typical inputs as construction of transportation and the operation and maintenance of the system. There are multiple outputs, simplified to person trips and freight trips, although of course each person trip is in some respects a different commodity. This view comports with Becker’s (1965) view that households use time in the production of commodities -- of which travel might be one.

Theory

To establish optimal emission levels for pollution, congestion or any other externality consider the following framework. All emissions, damages, and costs are from one or more sources $i$, subscripts are omitted for clarity.

$C(a)=C(z-e)\,\!$

where:

• $C(a)\,\!$ is the Cost of Abatement function with
• $C(a)'>0\,\!$ and $C(a)''\geq 0\,\!$

and

$D=D(e)\,\!$

where:

• $D(e)\,\!$ is the Cost of Damages function due to emissions .
• $e\,\!$is the actual emission from source.
• $z\,\!$ is the amount of emission at source in an uncontrolled state.
• $a=z-e\,\!$ is the amount of abatement at source.

Note if $a=0\,\!$, and thus $z=e\,\!$ the actual emissions equal the maximum amount possible.

The solution to the problem is to minimize the sum of damage costs and abatement costs or

$\min D(e)+C(z-e)\,\!$

${\frac {\delta D}{\delta e}}={\frac {\delta C}{\delta a}}\,\!$

which indicates a constant marginal demand function.

The following is true:

${\frac {\delta D}{\delta e}}={\frac {\delta C}{\delta a}}\bullet {\frac {\partial a}{\partial e}}\,\!$

$\therefore {\frac {\delta D}{\delta e}}={\frac {\delta C}{\delta a}}\,\!$

This states that the optimal amount of any externality is established by minimizing the sum of damage and abatement costs so we end up with E* amount of aggregate pollution.

If a profit maximizing firm were faced with an abatement charge they would internalize the externality or abate until the marginal cost of abatement were equal to the price of pollution or the change.

Government Standards

If the government wanted to establish a 'standard' it would require knowledge of:

• level of marginal damages
• Marginal Cost function of polluters

It would therefore appear that there is an informational advantage to pricing.

The solution which has been illustrated above also applies with:

• spatially differentiated damages
• non-linear damage functions
• non-competitive market settings

Standards dominate charged because

• Uncertainty with respect to the marginal damage function.
• Uncertainty with respect to the marginal abatement costs.

Uncertainty with respect to marginal damage function

Now consider the situation where the MC of abatement has been underestimated so the true MC of abatement lies above the estimated MC of abatement function. Consider a standards scheme. Using the estimated MC of abatement the emission level is set at e instead of e*. Thus, the emission level is too low relative to the optimum. With the level of abatement too high, the damages reduced due to having this lower level of emissions is eAce* but at the cost of much higher abatement costs of eBCe*. The net social loss will be ABC.

Alternatively, suppose the authority set a sub-optimal emission standard of e because it is using the erroneous MD function. With emissions at e rather than e*, we again end up with a net social loss of ABC. Therefore, uncertainty with respect to the marginal damage function provides NO ADVANTAGE to either scheme; pricing or standards.

Uncertainty with respect to marginal abatement costs

Now consider the situation where the MC of abatement has been underestimated so the true MC of abatement lies above the estimated MC of abatement function. Consider a standards scheme. Using the estimated MC of abatement the emission level is set at e instead of e*. Thus, the emission level is too low relative to the optimum. With the level of abatement too high, the damages reduced due to having this lower level of emissions is eAce* but at the cost of much higher abatement costs of eBCe*. The net social loss will be ABC

Now consider a pricing scheme. The authority would set the emission charge at EC by setting the MD function equal to the MC of abatement function. This would result in a level of emission of e; thinking this is the correct amount. But with a true MC of abatement at MCT the level of emissions which the charge EC will generate will be e'.

e' > e* so we have too high a level of emissions. Pollution damages will increase by the amount e*CDe' but the abatement costs will be reduced (because of higher allowed emissions) by e*CEe'. Therefore, the net social loss will be CDE. Generally, there is no reason to expect CDE = ABC but it has been shown that

$WL_{T}=WL_{q}=0.5\left({\frac {EC}{E}}\right)\bullet \left(\Delta e\right)^{2}\left({\frac {1}{\varepsilon _{D}}}+{\frac {1}{\varepsilon _{C}}}\right)$

where:

• $WL_{T}$ is the welfare loss from pricing
• $WL_{q}$ is the welfare loss from standards
• $\Delta e$ is $e'-e$
• $\varepsilon _{D}$ is the elasticity of the marginal damage function
• $\varepsilon _{C}$ is the elasticity of the marginal cost of abatement function

The welfare loss from pricing and standards will be equal if 1. = in absolute value or 2. $\Delta e=0$ or $MC_{A}=MC_{T}$

Standards will be preferred to charges when $WL_{T}-WL_{q}>0$ which occurs when

$\left|\varepsilon _{D}\right|<\left|\varepsilon _{C}\right|$.

If $\varepsilon _{C}>0$ charges are preferred while if $\varepsilon _{D}>0$ standards are preferred.

Rationale

The rationale for this is:

• if the MD function is steep (e.g. with very toxic pollution) even a slight error in $e$ will generate large damages. With uncertainty about costs, the chances of such errors is greater with a charging scheme.

• if the MD function is flat, a charge will better approximate marginal damages. If the damage function is linear, the optimal result is independent of any knowledge about costs.

• if the MC is steep, an ambitious standard could result in excessive costs to abators. A charge places an upper limit on costs.

Therefore, the KEY in this is charges set an upper limit on costs while standards set an upper limit on discharges.

Prices

Externality prices can take three forms:

1. use to optimize social surplus

2. use to achieve a predetermined standard at least cost]

3. use to induce compliance to a particular standard

Perhaps the best know 'cure' for the congestion externality facing most major cities has been advocated by economists; road pricing. Standards are achieved in this instance by continuing to build roads.

Measurement

The cost of an externality is a function of two equations. The first relates the physical production of the externality to the amount of transportation output. The second computes the economic cost per unit of externality. The amount of an externality produced by transportation is the result of the technology of the transportation, as well as the amount of defense and abatement measures undertaken. There are several issues of general concern in the physical production of externalities. They are classified as: fungibility, geography, life cycle, technology, and point of view. Each are addressed in turn.

Fungibility

“Is the externality fungible?” In other words, does the externality which is physically produced by the system under question have to be eliminated or paid for, or can something substitute for it. For example, a car may produce X amount of Carbon Dioxide. If carbon dioxide were not fungible, then that X would need to be eliminated, or a tax assessed based on the damage that X causes. However, if it were fungible, then an equivalent amount X could be eliminated through some other means (for instance, by installing pollution control on a factory or by planting trees). The second option may be cheaper, and this may influence the economic effects of the pollution generated.

Geography

“Over what area are the externalities considered?” “Is a cost generated by a project in California which is borne by those outside California relevant?” This is particularly important in estimating environmental costs, many of which are global in nature. If we try to estimate damages (rather than the protection costs of defense, abatement, and mitigation), this becomes particularly slippery. However, if we can assume fungibility, and use the cost of mitigation techniques, the measurement problem becomes much simpler. Ideally, we would obtain estimates for both protection and damages in order to determine the tradeoffs.

Life Cycle

In some respects we would like to view the life-cycle of the transportation system. But it becomes more difficult to consider the life-cycle of every input to the transportation system. The stages which may be considered include: Pre-production, construction, utilization, refurbishing, destruction, and disposal. Ignoring the life-cycle of all inputs may create some difficulties. Electric power will produce pollution externalities at production in a power plant, before it enters the transportation system. Thus, modes using electric power (rail, electric cars), would be at an advantage using this decision rule over modes which burn fuel during the transport process (airplanes, gasoline powered cars, diesel trains). This is true, though to a lesser extent, with other inputs as well.

Technology

The technology involved in transportation is constantly changing. The automobile fleet on the ground in 2000 will have very different characteristic than that in the year 1900 regarding the number of externalities produced. Hopefully, cars will be safer, cleaner, and quieter. Similar progress will no doubt be made in aircraft and trains. While the analysis will initially assume current technology, sensitivity tests should consider the effect that an improved fleet will have on minimizing externality production.

Macro vs. Micro Analysis Scale

Estimates for externalities typically come in two forms macro and micro levels of analysis. Macroscopic analysis uses national (or global) estimates of costs as share of gross domestic product (GDP), such as Kanafani (1983), Quinet (1990), and Button (1994). The data for microscopic analysis is far more dispersed. It relies on numerous engineering and empirical cost-benefit and micro-economic studies. By and large, this study is a microscopic analysis, though, on occasion, the macroscopic numbers will be used as benchmarks for comparison and estimates of data where not otherwise available. This will be true for both the physical production of externalities as well as their economic costs through damages borne or protection/attenuation measures. Once cost estimates are produced, they can be expanded to estimate the state-wide social costs of transport as a share of state product (California GDP), which can be compared with other national estimates.

Issues

Two important issues of concern in measuring the economic cost of externalities are: the basis over which the output is measured and the consistency of the measurement . When estimating the full cost of externalities, the amount of externality is not simply the amount of traffic on the road multiplied by some externality rate. Rather, it must be measured as the difference between what is generated systemwide with and without the facility. For instance, a new freeway lane will have several effects: diverting existing traffic from current facilities, inducing new traffic on the new facility, and inducing new/different traffic on the old facility. The amount of this change must be accurately determined with a general equilibrium approach to estimate demand. In a general equilibrium approach, the travel time/cost used to estimate the amount of demand is equal to the travel time/cost resulting from that demand. Switching traffic from an older facility to a newer facility may in fact reduce the amount of negative externalities generated. For instance, the number of accidents or their severity may decline if the new facility is safer than the old. On the other hand, the induced traffic, while certainly a benefit in that it increases commerce, also imposes new additional costs, more accidents, pollution and noise. It is the net change which must be considered.

When addressing the costs of externalities, the estimates used across all externalities should be consistent. Cost estimates contain implicit assumptions, particularly concerning the value of time, life, and safety. Key questions can be asked of any study:

• Is the value of life and health used in estimating the cost of accidents the same as used in estimating the human effects of pollution?

• Is the value of time used consistent between congestion costs and accidents? With congestion, many are delayed a small time, crashes (ignoring congestion implications), a few are delayed a long time.

Cost-Function Estimation Methods

Many approaches have been undertaken to estimate the costs of externalities. The first class of approaches we call “Damage” based methods, the second can be called “Protection” based methods. The damage based methods begin with the presumption that there is an externality and it causes X amount of damage through lower property values, quality of life, and health levels.

The protection methods estimate the cost to protect against a certain amount of the externality through abatement, defense, or mitigation. One example of a defense measure is thicker windows in a house to reduce noise from the road. An abatement measure would have the highway authority construct noise walls to reduce noise or require better mufflers on vehicles. A mitigation measure may only be applicable for certain types of externalities; e.g. increased safety measures that reduce accidents on one facility also offset the increased number of accidents on another facility.

Rising marginal costs are expected of protection measures. The first quantity of externality abated /defended/mitigated is cheaper than the second and so on because the most cost-effective measures are undertaken first. This is not to say there are no economies of scale in mitigating externalities within a given mitigation technology. It merely suggests that between technologies, costs will probably rise. The mitigation approach can be applied if we consider the externality fungible. Air pollution from the road may cause as much damage as an equivalent amount of pollution from nearby factories. The most cost effective approach to eliminating the amount of pollution produced by the road may come from additional scrubbers on the factory. While it may be prohibitively expensive to eliminate 100% of roadway pollution from the roadway alone, it may be quite reasonable to eliminate the same amount of pollution from the system. Determining the most effective method of mitigating each system-wide externality requires understanding the nature of its fungibility.

Neither of these two approaches (Damages or Protection) will necessarily produce a single value for the cost of a facility. It is more likely that each approach will produce a number of different cost estimates based on how it is undertaken and what assumptions are made. This reinforces the need for sensitivity analyses and a well-defined “systems” approach. We divide the techniques of costing into three main categories: revealed preference, stated preference, and implied preference. Revealed preference is based on observed conditions and how individuals subject to the externality behave, stated preference comes from surveys of individuals in hypothetical situations, while implied preference looks at the cost which is implied based on legislative, executive, or judicial decisions.

Revealed Preference

The revealed preference approach attempts to determine the cost of an externality by determining how much damage reduces the price of a good.

Revealed preference can also be used to estimate the price people pay for various protection (defense/ abatement) measures and the effectiveness of those measures. For instance, insulation costs a certain amount of money and provides a certain amount of effectiveness in reducing noise. The extent to which individuals then purchase insulation or double-glazed windows may suggest how much they value quiet. However, individuals may be willing to spend some money (but less than the cost of insulation) if they could ensure quiet by some other means which they do not control - but which may be technically feasible.

Hedonic Models: The most widely used estimates of the cost of noise are derived from hedonic models. These assume that the price of a good (for instance a home) is composed of a number of factors: square footage, accessibility, lot area, age of home, pollution, noise, etc. Using a regression analysis, the parameters for each of these factors are estimated. From this, the decline in the value of housing with the increase in the amount of noise can be estimated. This has been done widely for estimating the social cost of road noise and airport noise on individual homes. In theory, the value of commercial real estate may be similarly influenced by noise. In our literature review thus far, no study of this sort has been found. Furthermore, although noise impacts public buildings, this method cannot be used as a measure since public buildings are not sold. Similarly, when determining some of the costs of noise, one could investigate how much individuals might be willing to pay for vehicles which are quieter. Like a home, a hedonic model of vehicle attributes could be estimated. A vehicle is a bundle of attributes (room, acceleration, MPG, smooth ride, quiet, quality of workmanship, accessories) which influence its price, also an attribute.

Unit/Cost Approach: A simple method, the “unit cost (Rate) approach” is used often for allocating costs in transit. This method assigns each cost element, somewhat arbitrarily, to a single output measure or cost center (for instance, Vehicle Miles Travel, Vehicle Hours Travel, Number of Vehicles, Number of Passengers) based on the highest statistical correlation of the cost with output.

Wage/Risk Study: A means for determining the economic cost of risk to life or health or general discomfort is by analyzing wage/salary differentials based on job characteristics, including risk as a factor.

Time Use Study: This approach measures the time used to reduce some risk by a certain amount. For instance, seatbelts reduce the risk of injury or using pedestrian overpass may reduce the risk of being hit by a car. The time saved has a value, which may inform estimates of risk aversion.

Years Lost plus Direct Cost: This method estimates the number of years lost to an accident due to death and years lost from non-fatal injuries. It also the monetary costs of non-life damages. However, it defines life in monetary terms. While it may have some humanistic advantages in that it does not place a dollar value on life, defining life through dollars and sense may have some practical value. Defining life through dollars and sense may help us assess whether an improvement, with a certain construction cost and life-saving potential, is economically worthwhile.

Comprehensive: This accident costing method extends the Years Lost plus Direct Cost method by placing a value on human life. The value is assessed looking at the tradeoffs people make when choosing to conduct an activity a certain risk level versus another activity at a different risk, but different cost/time. Studies are based both on what people actually pay and what are willing to pay, and use a variety of revealed preference techniques. This is the preferred method of the US Federal Highway Administration.

Human Capital: The Human Capital approach is an accounting approach which focuses on the accident victim’s productive capacity or potential output, using the discounted present value of future earnings. To this are added costs such as property damage and medical costs. Pain and suffering can added as well. The Human Capital approach can be used for accidents, environmental health, and possibly congestion costs . It is used in the Australian study Social Cost of Road Accidents (1990) . However, Miller (1992) and others discount the method because the only effect of injury that counts is the out-of-pocket cost plus lost work and housework. By extension, it places low value on children and perhaps even a negative value on the elderly. While measuring human capital is a necessary input to the costs of accidents, it cannot be the only input.

Stated Preference

Stated preference involves using hypothetical questions to determine individual preferences regarding the economic costs of a facility. There are two primary classes of stated preference studies: Contingent Valuation and Conjoint Analysis.

Contingent Valuation: Perhaps the most straight-forward way of determining the cost of an externality is asking the hypothetical questions, “How much you would a person pay to reduce externality by a certain amount” or “How would a person pay to avoid the imposition of a certain increment of externality”. Jones-Lee (1990) has been the foremost investigator into this method for determining the cost of noise. This method can, in theory, be applied to any recipient of noise, although it has generally been asked of the neighbors (or potential neighbors) of a transportation facility.There are several difficulties with this approach. The first difficulty with any stated preference approach is that people give hypothetical answers to hypothetical questions. Therefore, the method should be calibrated to a revealed preference approach (with actual results for similar situations) before being relied upon as a sole source of information. The second regards the question of “rights”. For instance, someone who believes he has the right to quiet will not answer this question in the same way as someone who doesn’t. The third involves individuals who may claim infinite value to some commodity, which imposes difficulties for economic analysis.

Conjoint Analysis: To overcome the problems with contingent valuation, conjoint analysis has been used. Conjoint analysis requires individuals to tradeoffs between one good (e.g. quiet) and another (e.g. accessibility) has been used to better measure the cost of noise, as in Toronto by Gillen (1990) .

Implied Preference

There are methods for measuring the costs of externalities which are neither revealed from individual decisions nor stated by individuals on a survey. These are called implied preference because they are derived from regulatory or court-derived costs.

Regulatory Cost: Through government regulation, costs are imposed society with the aim of reducing the amount of noise or pollution or hazard is produced. These regulations include vehicle standards (e.g. mufflers) roadway abatement measures such as noise walls, as well as the many environmental regulations. By determining the costs and benefits of these regulations, the implicit cost of each externality can be estimated. This measure assumes that government is behaving consistently and rationally when imposing various standards or undertaking different projects.

Judicial Opinion and Negotiated Compensation: Similar to the implicit cost measure, one can look at how courts (judges and juries) weigh costs and benefits in cases which come before them. The cost per unit of noise or life from these judgments can be determined. This method is probably more viable in accident cases.

Incidence, Cost Allocation, and Compensation

This final set of topics deal with incidence (who causes the externality), cost allocation (who suffers from the externality), and compensation (how can the costs be appropriated and compensation paid fairly).

Incidence

The general model is that the costs can be generated by one of several parties and fall on one of several parties. The parties in this case are: the vehicle operators and carriers; the road, track, and airport operators; and the rest of society.

• Vehicle Operators and Carriers: bus company, truck company, driver of a car, railroad, airline
• Road/Track/Airport Operator: Department of Transportation, railroad, airport authority
• Society: the citizenry, government, citizens of other states/countries, the environment

This conceptual model is not concerned with anything smaller than the level of a vehicle. How costs on a vehicle are attributed to passengers in the vehicle, or the costs of freight carriage to the shipper, is not our concern. Similarly, ownership is not an issue, the operator of a vehicle may not be the owner, in the case, for instance, of a rented car. Obviously there is some overlap here between vehicle operators and road and track operators. In the case of American railroads, the firm which operates trains usually owns the track, although often a train will ride on tracks owned by a different railroad. Moreover, for some means of transportation, but not those considered here, there may be no vehicles (for example pipelines and conveyor belts.)

Costs can be imposed by any party on any party. As an illustration of how this works, we look at noise. Transportation noise is generated by vehicles in motion, and can affect any of the following classes: self, other vehicle users, and local society. There is noise generated by the roadway or the rail during construction, but this is ignored, and the noise does not actually hurt the road and track operators (except indirectly where they are held responsible for noise generated by vehicles and must build noise walls or other abatement measures.) A similar situation occurs with airports. Technically the planes make almost all of the noise, but the airport is held responsible. That noise is generated by wheels on pavement and thus depends in some respects on the roadway operator is also ignored.

• Vehicle operator on self, on other vehicles. For instance, one of the attributes of a vehicle (an auto say) is its quietness, this is reflected in the price of the vehicle. Quietness has two aspects: insulation, which protects the cab from noise generated by the car and other vehicles; and noise generation, which is how noisy the car is to itself and others. The noise generated by the vehicle and heard within the cab are internal costs, while those generated by the vehicle and heard by others is external to the vehicle operator, but internal to the transportation system.
• Vehicle operator on society. The noise generated by a vehicle negatively impacts the usefulness and flexibility of land uses nearby, where the impact declines with distance. The decline in utility is reflected in land values. The costs are clearly external to both the operator and the transportation system.

Cost Allocation

Clearly there are external costs, but it is not always clear who should bear them. This issue brings about questions of cost allocation. These include: objectives - for what reason are we allocating costs, methodology - how are we allocating costs, structure - how do we break down costs, and problems - how do we deal with the thorny issues of common and joint costs and cross-subsidies.

The first question that must be asked is what are the objectives of cost allocation. There are several contenders, which unfortunately are not entirely compatible. These include equity, efficiency, effectiveness, and acceptability.

The first consideration is equity or fairness. This concept raises a series of question summarized as “equity for whom”. Depending on how you slice it, different “fair” solutions are possible. The classic divisions are vertical vs. horizontal equity. Horizontal equity is a fair allocation of costs between users in the same sector, vertical equity is fairness across sectors. Are the costs allocated “fairly” between users, between facilities, between modes, between economic sectors? Is the burden for the project shared fairly between the economy and the environment? The second consideration is efficiency. Somewhat clearer than equity, efficiency still raises the same questions of “for whom.” Is the allocation efficient for the user, the operator, the state, the country? Does it consider inefficiencies, subsidies and taxes in other sectors of the economy, or other components of the transportation system? Efficiency can also be stratified into two categories: theoretical and practical.. The first ignores implementation (information and transaction) costs that rise with the number of charges imposed. Moreover, economists identify three kinds of efficiency: Allocative, which aims for the optimal mix of goods; Productive, which attempts to attain the minimum average cost; and Dynamic, which seeks long term optimal investment or capital rationing. Allocative efficiency may be thought of as congestion pricing, to ensure the optimal use of a transportation facility. Productive efficiency will attempt to raise enough money to operate and maintain the physical plant at the lowest cost. Dynamic efficiency will attempt to raise money to finance the facility, proactively or retroactively. To what extent these goals coincide is unclear.

Contrasted with efficiency is effectiveness. While the test of efficiency asks if the system is achieving its goals with minimum effort, the test of effectiveness asks if the system’s goals or output measures are consistent with broader societal goals. For instance, an efficient road may move traffic through a neighborhood at a high rate of speed, but this may be ineffective in meeting the broader social goal of a higher quality of life in the neighborhood, which the traffic disrupts. Costs can be allocated which achieve an efficient use of resources, but result in an ineffective or counter-productive system.

Added to this, we will consider the profit motive. If the facility is constructed by a profit seeking firm, prices will reflect an attempt at profit maximization in either a competitive, monopolistic, or oligopolistic environment.

A last consideration is acceptability. A system, which may have desirable attributes, if unimplemented, serves no-one. In the political world, tradeoffs and compromises must be made to achieve progress.

Costs can be allocated based on who causes them or by who receives benefit from them. There are pricing schemes reflecting both. There is a dichotomy between the methods of cost allocation suggested by economists and the approaches taken by engineers (as well as the official policy of the US government through modal cost allocation studies).

At least three economic approaches can be taken for allocating costs. The economic top-down approaches take equations of cost and allocate the results to users, these are: average total cost per user, average variable cost per user, and marginal cost (short run and long run), the last of which is favored by economists.

On the other hand, engineers working from the bottom-up break the system into components, which are assigned to users. Each mode or carrier has somewhat different methods for cost allocation. These are summarized below:

• Fixed Allocation - a set fee is charged based on some previous study
• Industry Agreed Upon (e.g. General Managers Associations Rules - rules allocating costs of freight cars on foreign rails, a pre-established agreement)
• Zero Allocation - user gets free ride on common costs and pays only attributable costs
• Proportional (New Investment/Long Range Pricing) - divides variable and fixed costs to users in proportion to use
• Minimum Cost of Service: Avoidable Cost Allocation (hierarchy costs/avoidable costs/separable costs/remaining benefits) - assigns to a beneficiary only the costs which could be avoided if the beneficiary did not use the service
• Minimum Cost of Service: Attributable Cost Allocation - assigns as cost allocation + share of common costs based on use.
• Minimum Cost of Service: Priority of Use Cost Allocation - assigns attributable cost allocation, but charges extra if priority is given to user or discounts if priority is taken from user (e.g. queue jumping)

In addition to the centralized cost allocation methods described above, there are other methods of allocation to users:

• Negotiated contracts - the parties negotiate the charge based on individual circumstances. This is often used in the rail industry where the trains of one carrier use the tracks of another.
• Arbitration - like a negotiated contract, but where a third party makes ultimate decision on the charge.
• Regulatory finding - A regulatory agency such as the former Interstate Commerce Commission gathers information and makes a decision as to appropriate rate. This is now most widely used in cases of monopoly oligopoly practice.
• Legislative finding - A legislature assumes the role of regulatory agency and prices and/or conditions of the cost allocation. An example of this is the adoption of taxes supporting the highway system, where gas taxes, vehicle licenses, and truck charges as well as tolls have to be approved by the state legislature.
• Judicial finding - After some dispute between parties (carrier vs. carrier, carrier vs. government or government vs. government) a court may be called on to make a final decision.
• Ramsey Pricing Rule - This rule would charge based on the customer’s elasticity of demand. The more elastic the customer (the more options he has the lower his price. So long as the short run marginal cost is covered, it may worthwhile for one firm to use this pricing rule to keep customers using their service rather than a competitors.
• Discriminating Monopolist/Oligopolist An unregulated monopoly discriminate among customers to obtain higher revenues (capture the consumer surplus). There are three classes of monopolistic discrimination: (1st degree, degree, 3rd degree).

The engineering and economic cost allocation discussed above allocate the costs to users. But there are alternative approaches:

• General Revenue: If transportation is to be subsidized, then the general public (including both users and non-users) can be charged a certain percentage of costs. This is seen when using general tax revenue for transportation.
• Value Capture: Similarly, another transfer occasionally used is a “value capture” approach, whereby nearby landowners are taxed based on the increase property value owing to a new transportation facility, this has been used in Angeles around new transit stations. In practice, some of each approach may be used.

Compensation

If individuals and organizations who cause externalities are to be charged, those who receive the unwanted noise, pollution, etc. should be compensated. To the extent that the recipients are amorphous, such as the environment, the collected funds should be expended in that sector for remediation of damages or their mitigation ahead of time. Also, the health damages from environmental damage are typically diffuse. On the other hand, it is fairly clear who suffers from noise. But the externality gets buried in the land price immediately after the opening (or perhaps announcement) of a facility. Therefore only the land owner at that time should receive compensation. Crashes result in damages to several classes of parties: those involved in crashes (and their families and insurance companies), commuters delayed by crashes (though this may be better treated in the congestion section), and society at large. Those involved are largely covered privately through the insurance sector, and care must be taken to avoid double-counting.

Congestion is typically divided into two classes: recurring and non-recurring. Non-recurring congestion is most often caused by incidents (traffic accidents, inclement weather). The value of time for these may be different, as recurring congestion probably entails less schedule delay since it is already accounted for by most commuters. Money raised from congestion pricing, in addition to reducing traffic volumes, can be used to expand capacity further to alleviate congestion. But this does not compensate those who now take a slower (but cheaper mode of transport) after road pricing is in effect. A question arises as to whether those individuals have some right to free travel which is being eliminated through pricing, or whether some general subsidies for travel are warranted. Congestion has further issues concerning pricing, for instance the peak vs. off-peak. When there is more traffic, each additional vehicle has more and more impact, suggesting higher tolls in the peak. However, the tolls will reduce demand, so an equilibrium solution to the problem is essential.

Social severance and visual impact are also amorphous. They will be difficult to price. To some extent for visual impact, the neighbors of a project can be identified and damages defined in terms of lower property values. In terms of the aesthetic quality of a trip, it may be conceptually possible to compare to parallel routes (a parkway vs. a freeway), one prettier than the other, and see if there is a difference in traffic volumes other than that explained by a route choice model. The difference in volume gives an implied choice of the value of the route in terms of additional time (and thus money), which may be significant in tourist areas. There is also a risk aspect to travel, drivers may choose certain roads which are through good areas, because they do not want to break down in isolated areas or perceived bad neighborhoods.

The social aspects of disruption of community (after taking into account net change in property value before and after infrastructure accounting for all of accessibility (increase or decrease), noise, and visual impact) is extremely difficult to determine. A political solution may need to be found to pricing and arranging for compensation.

Evidence on Pollution

Transportation sources in North America contribute approximately

• 47% of nitrogen oxide emissions (NOx)
• 71% of carbon monoxide emissions (CO)
• 39% of hydrocarbon emissions (HC)

Standards vs. Prices

To control most pollutants we have opted for standards rather than pricing. This is reflected in the 'level of allowed emissions' with catalytic converters on our vehicles.

Noise is another example where the U.S. has opted for a technological fix to achieve a standard. Europeans have, however, introduced noise charges at some airports for aircraft which exceed a particular noise level.

Private Cost v. Social Cost

The purpose of distinguishing private and social cost is to correct for real resource misallocation from economic agents actions which impose a cost (or benefit) on others in the market. The market provides no incentive for agents to take account of their actions.

The difference between private and social cost is that in making a decision a private individual will take account of the costs they face but will not consider the impact of their decision on others which may, in fact. impose a cost upon them. If this occurs an externality will misallocate resources since the economic agents are not forced to pay the cost they impose or does not receive any compensation for the benefits which they confer.

Full Cost Model

Based on:

An essential first step in examining transportation issues and in making sound decisions on transportation systems is to understand the full cost of transportation today, including the social costs of crashes, air pollution, noise, and congestion as well as the internal costs of providing and operating the infrastructure. Furthermore, if cross subsidies between modes, user groups, or areas of the country or states are to be avoided, and if users are to pay the full cost of providing and maintaining the transportation system, then it is important to know what proportion of total costs users currently pay and what proportion is borne by others. Such a complete assessment of the full cost of the different modes of transportation for intercity travel has been lacking. The development of cost models and estimates of the type presented in this research are essential to gauging the true costs of transportation in the different modes, and is a prerequisite to sound investment decisions.

The full cost calculation includes the cost of building, operating, and maintaining infrastructure, as well as carrier, user, and social costs. Social costs include noise, air pollution, and accident costs, as well as congestion costs. User costs include the cost of purchasing, maintaining and operating a vehicle such as a car, and the cost of travel time. We begin by developing a taxonomy for representing the full costs of transportation, independent of mode:

• Infrastructure Costs $C_{I}$- including capital costs of construction and debt service, and costs of maintenance and operating costs as well as service costs to government or private sector;
• Carrier Costs ${\displaystyle }$- aggregate of all payments by carriers in capital costs to purchase a vehicle fleet), and maintain and operate a vehicle fleet (COC), minus those costs (such as usage charges) which are transfers to infrastructure, which we label Carrier Transfers.
• User Money Costs $C_{U}$- aggregate of all fees, fares and tariffs paid by users in capital costs to purchase a vehicle, and money spent to maintain and operate the vehicle or to ride on a carrier (UOC); less those costs (such as fares) which are transfers to carriers or infrastructure, and accident insurance, which is considered under social costs, which we label User Transfers$T_{U}$.
• User Travel Time Costs $C_{T}$- the amount of time spent traveling under uncongested conditions multiplied by the monetary value of time.
• User Delay Costs$C_{D}$- the amount of time spent traveling under congested conditions minus the amount of time spent traveling in uncongested conditions multiplied by the monetary value of time.
• Social Costs - additional net external costs to society due to emissions $C_{E}$, crashes $C_{A}$, and noise $C_{N}$ and are true resource costs used in making and using transportation services;

The method used to estimate the full cost $C_{Full}$ of intercity travel will combine elements from a number of sources. Adding and subtracting the above factors, thereby avoiding double-counting, we have the following equation, the components of which will be dealt with in turn in the paper:

$C_{Full}=(C_{U}-T_{U})+C_{I}+C_{E}+C_{N}+C_{A}+C_{T}$

Key Issues

“Externalities” are Inputs to Production System. Clean Air, Quiet, Safety, Freeflow Time are used to produce a trip. The System has boundaries: Direct effects vs. Indirect effects Double Counting must be avoided

Selection of Externalities

Criteria: Direct Effects

Not Internalized in Capital or Operating Costs

External to User (not necessarily to system)

Result: Noise, Air Pollution, Congestion, Crashes

Not: Water Pollution, Parking, Defense ...

Approach

Noise

Measurement

Noise: Unwanted Sound

dB(A) = 10 log (P²/P_ref)

P: Pressure, P_ref: queitest audible sound

NEF: Noise Exposure Forecast is a function of number (frequency) of events and their loudness.

Generation

Amount of noise generated is a function of traffic flow, speed, types of traffic.

Additional vehicles have non-linear effect: e.g. 1 truck = 80 db, 2 trucks = 83 db, but sensitivity to loudness also rises

Noise decays with distance

Valuation

Hedonic Models: Decline of Property Values with Increase in Noise --> Noise Depreciation Index (NDI). Average NDI from many highway and airport studies is 0.62. For each unit increase in dB(A), there is a 0.62% decline in the price of a house

Integration

Noise Cost Functions ($/pkt) : f(Quantity of Noise, House Values, Housing Density, Interest Rates)

Using “reasonable” assumption, this ranges from $0.0001/vkt - $0.0060/vkt for highway. Best guess = $0.0045/pkt. For air, about the same, $0.0043/pkt.

Air Pollution

Measurement

Air Pollution Problems: Smog, Acid Rain, Ozone Depletion, Global Climate Change.

EPA “Criteria” Pollutants: HC (a.k.a. VOC, ROG), NOx, CO, SOx, PM10

Other Pollutants: CO2

Generation

Mode	Pax km	HC kg, M	CO kg,M	NOx kg, M	C,Ton
		(gm/pkt)	(gm/pkt)	(gm/pkt)	M
					(gm/pkt)
Highways	5.4 x1012	5,118	32,690	5,945	263.2
		-0.95	-6.053	-1.11	-46
Jets	5.8 x1011	54	163	72.7	59.2
		-0.093	-0.28	-0.13	-100
Total		6,409	39,972	7,918
Transport
Total All		18,536	60,863	19,890
Sources

Valuation

Local Health Effects, Material and Vegetation Effects, Global Effects Greatest Uncertainty in Global Effects, Proposed “Carbon Tax” have 2 orders of magnitude differences

Integration

Pollutant	Air Transportation Cost	Highway Transportation Costs
	($/pkt)	($/vkt)
PM10	---	$0.000066
SOx	---	$0.00024
HC	$0.00012	$0.0030
CO	$0.0000018	$0.000049
NOx	$0.00017	$0.0010
Carbon	$0.00058	$0.00026
TOTAL	$0.00087	$0.0046

Congestion

Measurement

Time: Congested, Uncongested

Congested Time Increases as Flow Approaches, Exceeds “Capacity”

Uncongested Time: Freeflow Time + Schedule Delay

Generation

Air Transportation: Delay vs. Usage

Valuation

The value of time depends on a number of factors (Hensher 1995). Among them are the mode of travel, the time of day, the purpose (business, non-business) of the trip, the quality or level of service of the trip (including speed), and the specific characteristics of the trip-maker, including income. Furthermore, the value of time saved probably depends on the amount of time saved - 60 people saving 1 minute may not be worth the same as 1 person saving 60 minutes. Time in motion is valued differently than time spent waiting. Similarly schedule delay, the amount of time between when one wants to depart and the next scheduled service (bus, train, plane) also has a value associated with it. Unexpected delays are more costly than the expected, since those are built into decisions. All of these factors need to be considered in a detailed operational analysis of the costs of travel time and congestion.

Value of Time is a function of mode, time of day, purpose, quality of service, trip-maker.

Wide range, typically $50/hr air, $30/hr car. (Business Trips more valuble than Personal Trips).

On other hand, average hourly PCI rate (40 hour week) gives $10/hr

Integration

Time Cost Functions:

TC = VoT Qh ( Lf/ Vf + a (Qh / Qho)b)

highway: a=0.32, b=10

air: a=2.33, b=6

Crashes

Measurement

Number of Crashes by Severity Multiple Databases (NASS, FARS) Multiple Agencies (NHTSA, NTSB), + states and insurance agencies Inconsistent Classification Non-reporting

Generation

Crash Rates, Functions Highway: Crash Rate = f(urban/rural, onramps, auxiliarly lanes, flow, queueing) Air: Crash Rate = f( type of aircraft)

Valuation

The principal means for estimating the cost of crashes is to estimate their damage costs. The method presented here uses a comprehensive approach which includes valuing years lost to the accident as well as direct costs. Several steps must be undertaken: converting injuries to years of life, developing a value of life, and estimating other costs. Placing a value on injury requires measuring its severity. Miller (1993) describes a year of functional capacity (365 days/year, 24 hours/day) as consisting of several dimensions: Mobility, Cognitive, Self Care, Sensory, Cosmetic, Pain, Ability to perform household responsibilities, and Ability to perform wage work. The following Tables show the percent of hours lost by degree of injury, and the functional years lost by degree of injury.

Percentage of Hours Lost to Injuries by Degree of Injury

Type of Activity	Modest	Major	Fatal	Total
Functioning	18.0	40.7	41.3	100.0
HH Production	25.2	22.1	52.7	100.0
Work	21.7	19.1	59.2	100.0

source Miller (1991) p.26

Functional Years lost by Degree of Injury

Degree of Injury	Per Injury	Percent of Lifespan	Per Year	Percent of Annual Total
1. Minor	0.07	0.15	316,600	10.7
2. Moderate	1.1	2.3	587,700	20.0
3.Serious	6.5	13.8	1,176,700	40.0
4. Severe	16.5	35.0	446,700	15.2
5. Critical	33.1	70.0	413,800	14.1
Avg. Nonfatal	0.7	1.5	2,941,500	100.0
Fatal	42.7	100.0	2.007,000

source Miller (1991) p29 note: expected lifespan for nonfatally injured averages 47.2 years

Federal Highway Administration uses the following:

MAIS Level	Severity	Fraction of VSL
MAIS 1	Minor	0.0020
MAIS 2	Moderate	0.0155
MAIS 3	Serious	0.0575
MAIS 4	Severe	0.1875
MAIS 5	Critical	0.7625
MAIS 6	Fatal	1.0000

source:

Central to the estimation of costs is an estimate of the value of life (or value of a statistical life). Numerous studies have approached this question from various angles. Jones-Lee (1988) provides one summary, with an emphasis on British values from revealed and stated preference studies. The FAA (1989) provides another summary. He finds the range of value of life to vary by up to two orders of magnitude (a factor of 100). Miller’s (1991) summary is reproduced below, with numbers updated to 1995 dollars.

Estimated Value of Life by Type of Study

Type of Study	Value of Life ($)
(1988 dollars)	Value of Life ($)
(1995 dollars)
Average of 49 studies	2.2 M	2.9 M
Average of 11 auto safety studies	2.1 M	2.7 M
Study Type
Extra wages for risky jobs (30 studies)	1.9-3.4 M	2.5 - 4.4 M
Market demand vs. price
safer cars	2.6 M	3.4 M
smoke detectors	1.2 M	1.6 M
houses in less polluted areas	2.6 M	3.4 M
life insurance	3.0 M	3.9 M
wages	2.1 M	2.7 M
Safety behavior
pedestrian tunnel use	2.1 M	2.7 M
safety belt use (2 studies)	2.0 - 3.1 M	2.6 - 4.0 M
speed choice (2 studies)	1.3 -2.2 M	1.7 - 2.9 M
smoking	1.0 M	1.3 M
Surveys
Auto safety (5 studies)	1.2-2.8 M	1.6 - 3.6 M
Cancer	2.6 M	3.4 M
Safer Job	2.2 M	2.9 M
Fire Safety	3.6 M	4.7 M

Source: Miller (1990), Note: in millions (M) of after-tax dollars ($1995 = $1988 * 1.3).

Currently (as of 2008 $) FHWA uses $5.8 M, which is the average of several recent studies.

Integration

Highway Accident Costs estimates range from $0.002 - $0.09/pkt. Our estimate is $0.02/pkt. Urban / rural tradeoff. Urban more but less severe crashes. Air Accident Costs $0.0005/pkt.

Summary

Costs in $ per passenger km traveled.

Cost Category	Air System	Highway System
Noise	$0.0043	$0.0045
Air Pollution	$0.0009	$0.0031
Crashes	$0.0004	$0.0200
Congestion	$0.0017	$0.0046
TOTAL	$0.01	$0.03

High Uncertainty About Valuation

Costs Vary with Usage

Accounting, Difficult, but necessary to avoid double counting.

Thought Question: Value of Life

Suppose there is a road improvement which will save 1 life per year, reducing the number of fatalities from 2 to 1 per year (out of 1000 people using the road). Assume all travelers are identical. What value of life should be used in the analysis?

Normally, we would do the equivalent of trying to compute for each traveler what is the willingness to pay for a 50% reduction in the chance of death by driving (from 2 in 1000 to 1 in 1000), and multiply that by the 1000 people whose chance of dying is reduced.

An alternative approach is to figure out the willingness to pay for the driver whose life is saved. So how much would you pay to avoid dying (with certainty) (i.e. what is your Willingness to Pay)? The answer to the first question is usually taken to be all of your resources (you would pay you everything so I won't kill you).

Alternatively how much can I pay you to allow you to let me kill you (Willingness to Accept)? The answer to this second question is: I would have to pay you an infinite amount of money in order for you to let me kill you.

Both of those sums of money (everything or infinity) likely exceed the willingness to pay to reduce the likelihood of dying with some probability, multiplied by the number of people experiencing it.

In economic terms, we are comparing the area under the demand curve (the consumer's surplus) for life (which has a value asymptotically approaching infinity as the amount of life approaches 0 (death approaches certainty) for a single individual, with the marginal change in the likelihood of survival multiplied by all individuals (i.e. the quadrilateral between the y-axis of price and the same demand curve, between Pb and Pa) which describes the change in price for a change in survival).

On the one hand, using the marginal change for everyone rather than total change for the one person whose life is saved, we will give a lower value to safety improvements. On the other hand, the value of life to the individual himself is much higher than the value of life of that individual to society at large.

Utility

Utility is the economists representation of whatever consumers try to maximize. Consumers may want more of one thing and less of another. ...

Indifference Curves

Indifference curve

Demand depends on utility. Utility functions represent a way of assigning rankings to different bundles such that more preferred bundles are ranked higher than less preferred bundles. A utility function can be represented in a general way as:

$U=U(x_{1},x_{2})=x_{1}x_{2}\,\!$

where $x_{1}$ and $x_{2}$ are goods (e.g. the net benefits resulting from a trip)

An indifference curve is the locus of commodity bundles over which a consumer is indifferent. If preferences satisfy the usual regularity conditions (discussed below), then there is a utility function $U(x_{1},x_{2})$ that represents these preferences. Points along the indifference curve represent iso-utility. The negative slope indicates the marginal rate of substitution (MRS):

$MRS=-{\frac {\Delta x_{2}}{\Delta x_{1}}}\,\!$

Substitutes and Complements

Substitute goods

Complements curve

Substitutes would be represented by :

$U(x_{1},x_{2})=ax_{1}+bx_{2}\,\!$

where the slope of the indifference curve would be = -a/b.

In graphic terms substitutability is greater the more the indifference curves approach a straight line. Perfect substitutability is a straight line indifference curve (e.g. trips to work by mode A or mode B).

Complements are represented by:

$U(x_{1},x_{2})=min(x_{1},x_{2})\,\!$

The more complementary the more the indifference curves approach a right angle curve; perfect complementarity would have a right angle indifference curve (eg. left and right shoes, trips from home to work and work to home)

Trade Game

The trade game is a way of examining how economic trading of resources affects individual utility. Imagine the economy consists of the following resources (denoted by colored slips of paper)

• White
• Purple
• Brown
• Orange
• Blue
• Gray
• Green
• Yellow
• Gold

The objective of the game is to maximize your gains in utility.

Define A Utility Function for Yourself

$U=f({\text{White, Purple, Brown, Orange, Blue, Gray, Green, Yellow, Gold}})$

You are handed an assortment of resources

Measure your utility

Trade with others in the class (15 minutes) Record your trades.

At the end of the trading period measure your utility again. Compute your absolute and percentage increase.

Record scores on the board

Discuss

Is there a better way to allocate resources?

Preference Maximization

Graphical

Budget constraints

Budget curve moves outward

Slope of budget curve changes

Optimization of utility

Utility maximization involves the choice of bundles under a resource constraint. For example, individuals select the amount of goods, services and transportation by comparing the utility increase with an increase in consumption against the utility loss associated with the giving up of resources (or equivalently forgoing the consumption which those resources command).

Often one price is taken to be 1, and one good is taken to be money. An income increase can be represented by the outward movement of the budget line.

An increase in the price of good $X_{1}$ can be represented by a change in the slope of the budget line (still anchored at one end).

In graphic terms the process of optimization is accomplished by equating the rate at which an individual is willing to trade off one good for another to the rate at which the market allows him/her to trade them off. This can be represented in the following graph

The individual maximizes utility by moving down the budget constraint to that point at which the slope of the budget line ($-P_{1}/P_{2}$) which is the rate of exchange dictated by the market is just equal to the rate at which the individual is willing to trade the two goods off. This is the slope of the indifference curve or the marginal rate of transformation (MRT). A point such as 'e' is an equilibrium point at which utility is being maximized.

Equilibrium is the tangency between the indifference curve/utility and the budget constraint.

Optimization

As an optimization problem, this can be written:

${\text{Maximize}}U(X)\,\!$

subject to:

$px\leq m\,\!$

$x$ is in $X$

where:

• $p$ = price vector,
• $x$ = goods vector,
• $m$ = income

(Because of non-satiation, the constraint can be written as px=m.) This kind of problem can be solved with the use of the Lagrangian:

$\Lambda =U(X)-\lambda (px-m)\,\!$ where

• $\lambda$ is the Lagrange multiplier

Take derivatives with respect to $x$, and set the first order conditions to 0

${\frac {\partial \Lambda }{\partial x_{i}}}={\frac {\partial U(X)}{\partial x_{i}}}-\lambda p_{i}=0\,\!$

Divide to get the Marginal rate of substitution and Economic Rate of Substitution

$MRS={\frac {\frac {\partial U(X)}{\partial x_{i}}}{\frac {\partial U(X)}{\partial x_{j}}}}={\frac {p_{i}}{p_{j}}}=ERS\,\!$

Example: Optimizing Utility

${\text{Max}}U=x_{1}x_{2}\,\!$

${\text{s.t.}}m=p_{1}x_{1}+p_{2}x_{2}\,\!$

$\Lambda =x_{1}x_{2}-\lambda (p_{1}x_{1}+p_{2}x_{2}-m)\,\!$

${\frac {\partial \Lambda }{\partial x_{1}}}=x_{2}-\lambda p_{1}=0\,\!$

${\frac {\partial \Lambda }{\partial x_{2}}}=x_{1}-\lambda p_{2}=0\,\!$

Solving

${\frac {x_{2}}{p_{1}}}={\frac {x_{1}}{p_{2}}}\,\!$

or

$p_{1}x_{1}{\text{ }}={\text{ }}p_{2}x_{2}\,\!$

substituting into the budget constraint:

$m=2p_{1}x_{1}\,\!$

$x_{_{1}}^{*}={\frac {m}{2p_{1}}}\,\!$

$x_{_{2}}^{*}={\frac {m}{2p_{2}}}\,\!$

Demand, Expenditure, and Utility

Indirect Utility

The Marshallian Demand relates price and income to the demanded bundle. This is given as $x(p,m)$. This function is homogenous of degree 0, so if we double both $p$ and $m$, $x$ remains constant. We can develop an indirect utility function:

$v(p,m)=maxU(X)\,\!$

subject to: $px=m\,\!$

where X that solves this is the demanded bundle

Example: Indirect Utility

$\left({\frac {m}{{\text{2}}p_{1}}}\right)\left({\frac {m}{{\text{2}}p_{2}}}\right)={\frac {m^{2}}{4p_{1}p_{2}}}\,\!$

taking a monotonic transform:

$=\left({\frac {1}{4}}\right)\left(2\ln \left(m\right)-\ln \left(p_{1}\right)-\ln \left(p_{2}\right)\right)\,\!$

which increases in income and decreases in price

where the $X$ that solves this is the demanded bundle

Properties

Properties of the indirect utility function $v(p,m)$

• is non-increasing in $p$, non-decreasing in $m$
• homogenous of degree 0
• quasiconvex in $p$
• continuous at all $p>>0,m>0$

Expenditure Function

The inverse of the indirect utility is the expenditure function $e(p,u)={\text{min}}px\,\!$

subject to: $u(x)\geq u\,\!$

Properties of the expenditure function $e(p,u)$:

• is non-decreasing in $p$
• homogenous of degree 1 in $p$
• concave in $p$
• continuous in $p$ for $p>>0$

Roy's Identity

The Hicksian Demand or compensated demand is denoted h(p,u).

$h_{i}(p,u)={\frac {\partial e(p,u)}{\partial p_{i}}}\,\!$

vary price and income to keep consumer at fixed utility level vs. Marshallian demand. Roy's Identity allows going back and forth between observed demand and utility

$x_{i}(p,m)=-{\frac {\frac {\partial v(p,m)}{\partial p_{i}}}{\frac {\partial v(p,m)}{\partial m}}}\,\!$

Example (continued)

$x_{1}(p,m)=-{\frac {{}^{\partial V}\!\!\diagup \!\!{}_{\partial p}\;}{{}^{\partial V}\!\!\diagup \!\!{}_{\partial m}\;}}=-{\frac {-{}^{m^{2}}\!\!\diagup \!\!{}_{4p_{1}^{2}p_{2}^{}}\;}{{}^{2m}\!\!\diagup \!\!{}_{4p_{1}^{}p_{2}^{}}\;}}={\frac {2m}{p_{1}}}\,\!$

$x_{2}(p,m)={\frac {2m}{p_{2}}}\,\!$

Equivalencies

$e(p,v(p,m))=m\,\!$ the minimum expenditure to reach $v(p,m)$ is $m$

$v(p,e(p,u))=u\,\!$ the maximum utility from income $e(p,u)$ is $u$

$x_{i}(p,m)=h_{i}(p,v(p,m))\,\!$ Marshallian demand at $m$ is Hicksian demand at $v(p,m)$

$h_{i}(p,u)=x_{i}(p,e(p,u))\,\!$ Hicksian demand at $u$ is Marshallian demand at $e(p,u)$

Measuring Welfare

Money Metric Indirect Utility Function

The Money Metric Indirect Utility Function tells how much money at price p is required to be as well off as at price level q and income m. Define it as

$\mu (p;q,m)=e(p,v(q,m))\,\!$

Equivalent Variation

$EV=\mu (p^{0};p^{1},m^{1})-\mu (p^{0};p^{0},m^{0})\,\!$

note 1 indicates after, 0 indicates before

Current prices are the base, what income change will give equivalent utility

Compensating Variation

$CV=\mu (p^{1};p^{1},m^{1})-\mu (p^{1};p^{0},m^{0})\,\!$ New prices are the base, what income change will compensate for price change

Consumer's Surplus

Utility and Consumer's Surplus

$\Delta CS=\int \limits _{p^{0}}^{p^{1}}{x(t)dt}\,\!$

Generally

$EV\geq CS\geq CV\,\!$

When utility is quasilinear ($U=U(X1)+X0)\,\!$, then:

$EV=CS=CV\,\!$

Arrow's Impossibility Theorem

Arrow's Impossibility Theorem An illustration of the problem of aggregation of social welfare functions:

Three individuals each have well-behaved preferences. However, aggregating the three does not produce a well behaved preference function:

• Person A prefers red to blue and blue to green
• Person B prefers green to red and red to blue
• Person C prefers blue to green and green to red.

Aggregating, transitivity is violated.

• Two people prefer red to blue
• Two people prefer blue to green, and
• Two people prefer green to red.

What does society want?

Preferences

Consumption Bundles

Define a consumption set X, e.g. {house, car, computer},

'x', 'y', 'z', are bundles of goods, such as x{house,car}, y{car, computer}, z{house, computer}.

Goods are not consumed for themselves but for their attributes relative to other goods

We want to find preferences that order the bundles. Utility is ordinal, so we only care about which is greater, not by how much.

Conditions

There are several Conditions on preferences to produce a continuous (well-behaved) utility function.

• Completeness: Either $x{\underline {\succ }}y$ (Read x is preferred to y) or $y{\underline {\succ }}x$ or both
• Reflexive: $x{\underline {\succ }}x$
• Transitive: if $x{\underline {\succ }}y$ and $y{\underline {\succ }}z$ then $x{\underline {\succ }}z$ (This poses a problem for social welfare functions)
• Monotonicity: If $x\geq y$then $x{\underline {\succ }}y$
• Local Non-satiation: More is better than less
• Convexity: if $x{\underline {\succ }}y$ and $y{\underline {\succ }}z$ then $tx+(1-t)y{\underline {\succ }}z$
• Continuity: small changes in input beget small changes in output. The preference relation ${\underline {\succ }}$ in X is continuous if it is preserved under the limit operation

The function f is continuous at the point a in its domain if:

• ${\underset {x\to a}{\mathop {\lim } }}\,f\left(x\right)\,\!$ exists

• ${\underset {x\to a}{\mathop {\lim } }}\,f\left(x\right)=f\left(a\right)\,\!$

If 'f' is not continuous at 'a', we say that 'f' is discontinuous at 'a'.

Further Reading

• Utility Applied to Mode Choice (Fundamentals of Transportation wikibook)

Demand

Demand

Individual Demand Functions

Individual demand curve

Engel Curve

Budget Line Pivots: To get the demand curve, change relative price (say P1). The Budget Line Pivots and the equilibrium solution changes. Thus consumer demand depends on price and income. Plot $P_{1}$ vs. $X_{1}*$, this is the conventional demand curve we began with.

The demand function is a relationship between the quantity of a good/service that an individual will consume at different prices, holding other prices and income constant. Every point on the demand function is a utility maximizing point. In effect, the demand curve is a translation from utility metric space into dollar metric space. Thus, point 'e' in the diagram above is a point on the demand curve.

To construct the demand curve simply vary the price of one good holding the price of other goods and income constant. In graphical terms this is represented as in the diagrams below. Note that the equilibrium points in the upper diagram have their counterparts in 'quantity space' in the lower diagram. Therefore, this shows that prices or expenditure information provides a measure of people's preferences and can be used in making assessments with respect to valuation.

An Engel curve is also associated with the development of the demand curve from the utility maximizing framework. An Engel curve is the locus of combinations of goods that an individual would consume if they were faced with changes in income holding all prices constant. Pictorially this would mean a parallel shift in the budget constraint either up or down if income rises or falls, respectively. This Engel curve is also known as an income-consumption curve.

• normal goods: the Engel curve is upward sloping
• inferior goods: Engel curve is downward sloping
• perfect substitutes: Engel curve is positively slope with a slope value of $P_{1}$
• perfect complements: Engel curve is positively sloped with a slope equal to $P_{1}+P_{2}$

Homothetic Preferences depend only on the ratio of goods in the consumption bundle. This means that homothetic preferences will yield straight line Engel curves which pass through the origin. This has the interpretation that if income goes up by a factor $t$, the demand bundle goes up by a factor $t$. Log-linear preferences are an example of homothetic preferences but not all homothetic preferences are log-linear.

The demand curve is defined as the relationship between price and quantity in which the quantity demanded is the unknown and the price is the exogenously given variable. The relationship is represented as: $Q=Q(P)$

The inverse demand curve is simply the monotone transformation of the 'ordinary' demand curve. The inverse demand curve indicates, for each level of demand for good 1, the price which would have to be charged for the consumer to consume a given amount. The inverse demand curve is represented as: $P=P(Q)$

Aggregate Demand

Aggregation of demand of private goods

Aggregation of demand of public goods

Moving from individual to aggregate demand requires that we sum individual demands in some way. The level of aggregation is determined by the nature of the issue at hand. Demand functions can be defined over socio-economic groups, cities, states and economy wide. There are numerous issues of 'aggregation' not least of which is how one handles the diversity of consumer preferences while aggregating.

One of the interesting issues is how to aggregate given the nature of the good. This is an issue in transportation since some people consider transportation infrastructure 'quasi-public' goods.

Private goods: if I increase my consumption I reduce the amount available for anyone else, the aggregation from individual to aggregate is to sum horizontally. (Left) This reflects the scarcity of the good.

Public goods: if I increase my consumption, the amount available remains, the aggregation from individual to aggregate should be vertical. (Right) P=society’s willingness to pay

Input Demand Theory

Isoquant and Isocost Curves

To get the cost curve, change the output level, then the isoquant moves and minimum cost is achieved at different K-L combinations.

To date we have looked at demand for consumers. Demand for firms applies similar ideas. For instance, a firm may need to choose a trucking company to ship its goods. It can either approach the problem as cost minimization or profit maximization, which are called Duals of each other, and when solved will produce the same answer.

Cost minimization: given the output level Q', minimize costs.

An example of this constrained optimization problem just illustrated is:

${\begin{aligned}&{\text{Min C }}={\text{ }}wL+rK\\&{\text{s}}{\text{.t}}{\text{. }}F(K,L)=Q'\\\end{aligned}}$

where

• K = Kapital
• L = Labor
• w = wage rate
• r = interest rate

The Marginal Rate of Technical Substitution (MRTS) = w/r.

Plot Q vs. C(Q)

In a competitive market, and a whole set of associated assumptions, firms maximize profits by producing when

Marginal Cost = Marginal Revenue.

Profit $\Pi =PQ-C(Q)$.

Elasticity

The utility function is a representation of consumer preferences and a demand function is the mapping of utility (and hence preferences) into quantity space. The elasticity is a summary measure of the demand curve and it is therefore influenced to a great extent by the underlying preference structure. Elasticity is defined as a proportionate change in one variable over the proportionate change in another variable. It, therefore, provides a measure of how sensitive one variable is to changes in some other variable.

For example:

• How sensitive are people to purchasing transit tickets if the fare went up 5%, 10% or 50%?
• How would the demand for housing change if mortgage rates fell by 30%
• How would the demand for international air travel change if airfares went up 15%?

All of these questions are really asking, "what is the elasticity of demand with respect to some variable"?

Price elasticity of demand (PED) can be defined as

$E_{d}={\frac {\%\ {\mbox{change in quantity demanded}}}{\%\ {\mbox{change in price}}}}={\frac {\Delta Q_{d}/Q_{d}}{\Delta P/P}}$

Own-price Elasticity

the price elasticity of demand (own price elasticity) is defined as:

$\varepsilon _{ii}={\frac {p_{i}\Delta q_{i}}{q_{i}\Delta p_{i}}}={\frac {p_{i}\partial q_{i}}{q_{i}\partial p_{i}}}$

Note that dq/dp is the slope of the demand function so unless there is a very particular type of demand function the slope is not the same as the elasticity.

In general, own price elasticity is negative. An increase in $P_{i}$ should increase the consumption of $Q_{i}$, (all else equal). However it is often referred to as positive, this is just confusing. All goods have a price elasticity, however, if the elasticity is less than -1, than the good is called elastic and if the elasticity is between 0 and -1, then the good is inelastic.

This is important when looking at the effect of fuel prices on travel demand.

Cross-price Elasticity

Cross price elasticity examines how the quantity of good i consumed changes as the price of j changes:

$\varepsilon _{ij}={\frac {p_{j}\Delta q_{i}}{q_{i}\Delta p_{j}}}={\frac {p_{j}\partial q_{i}}{q_{i}\partial p_{j}}}$

If $P_{j}$ increases and $Q_{i}$ increases, then $Q_{i}$ and $Q_{j}$ are substitutes. If $P_{j}$ decreases and $Q_{i}$ increases, then $Q_{i}$ and $Q_{j}$ are complements

This is important in examining modal competition.

Income Elasticity

$\varepsilon _{iY}={\frac {Y\partial q_{i}}{q_{i}\partial Y}}$

If Y increases and Qi increases, then Qi is a normal good. If Y increases and Qi decreases then Qi is an inferior good.

Examples are auto ownership, and the difference between new and used cars.

References

• Gillespie, Andrew (1 March 2007). Foundations of Economics. Oxford University Press. ISBN 9780199296378. Retrieved 28 February 2010.

• Gwartney, James D.; Stroup, Richard L.; Sobel, Russell S. (14 January 2008). Economics: Private and Public Choice. Cengage Learning. ISBN 9780324580181. Retrieved 28 February 2010. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

• Parkin, Michael; Powell, Melanie; Matthews, Kent (2002). Economics. Harlow: Addison-Wesley. ISBN 0-273-65813-1.

Positive externalities

Remember, an externality is a cost or benefit incurred by a party due to the decision or purchase of another, who neither obtains the consent of the said party, nor effectively considers the costs and/or benefits to the said party in the decision.

Positive and Negative Feedback: A Systems Approach

Equilibrium in a Negative Feedback System

Negative feedback loop

Illustration of equilibrium between supply and demand

Supply and Demand comprise the economist's view of transportation systems. They are equilibrium systems. What does that mean?

Transportation costs both time and money. These costs are represented by a supply curve, which rises with the amount of travel demanded. As described above, demand (e.g. the number of vehicles which want to use the facility) depends on the price, the lower the price, the higher the demand. These two curves intersect at an equilibrium point. In the example figure, they intersect at a toll of $0.50 per km, and flow of 3000 vehicles per hour. Time is usually converted to money (using a Value of Time), to simplify the analysis.

Costs may be variable and include users' time, out-of-pockets costs (paid on a per trip or per distance basis) like tolls, gasolines, and fares, or fixed like insurance or buying an automobile, which are only borne once in a while and are largely independent of the cost of an individual trip.

It means the system is subject to a negative feedback process:

An increase in A begets a decrease in B. An increase B begets an increase in A.

Disequilibrium

Positive feedback loop (virtuous circle)

Positive feedback loop (vicious circle)

However, many elements of the transportation system do not necessarily generate an equilibrium. Take the case where an increase in A begets an increase in B. An increase in B begets an increase in A. An example where A an increase in Traffic Demand generates more Gas Tax Revenue (B) more Gas Tax Revenue generates more Road Building, which in turn increases traffic demand. (This example assumes the gas tax generates more demand from the resultant road building than costs in sensitivity of demand to the price, i.e. the investment is worthwhile). This is dubbed a positive feedback system, and in some contexts a "Virtuous Circle", where the "virtue" is a value judgment that depends on your perspective.

Similarly, one might have a "Vicious Circle" where a decrease in A begets a decrease in B and a decrease in B begets a decrease in A. A classic example of this is where (A) is Transit Service and (B) is Transit Demand. Again "vicious" is a value judgment. Less service results in fewer transit riders, fewer transit riders cannot make as a great a claim on transportation resources, leading to more service cutbacks.

These systems of course interact: more road building may attract transit riders to cars, while those additional drivers pay gas taxes and generate more roads.

One might ask whether positive feedback systems converge or diverge. The answer is "it depends on the system", and in particular where or when in the system you observe. There might be some point where no matter how many additional roads you built, there would be no more traffic demand, as everyone already consumes as much travel as they want to. We have yet to reach that point for roads, but on the other hand, we have for lots of goods. If you live in most parts of the United States, the price of water at your house probably does not affect how much you drink, and a lower price for tap water would not increase your rate of ingestion. You might use substitutes if their prices were lower (or tap water were costlier), e.g. bottled water. Price might affect other behaviors such as lawn watering and car washing though.

Examples of Feedback Systems

We explore a few examples related to urban growth, accessibility, electric vehicle adoption, and urban transit.

Traffic congestion and Travel Demand (-) An example of a negative feedback system is Traffic Congestion and Traffic Demand. More congestion limits demand, but more demand creates more congestion.

Bus Bunching (+) An example of a positive feedback system is Bus bunching. Buses operating with high frequency tend to bunch. A lead bus picks up passengers, each passenger makes the bus slower. As the bus approaches the next stop, there are more passengers waiting. The following bus in contrast gets faster as there are fewer and fewer passengers waiting at each stop, since the previous bus is later and gets more boardings. Eventually the buses bunch together. This simulation illustrates and explains the phenomenon.

Agglomeration Economies and City Growth (+) Economists have sought to understand why cities grow and why large cities seem to be at an advantage relative to others. One explanation that has received much attention emphasizes the role of agglomeration economies in facilitating and sustaining city growth. The clustering of firms and workers in cities generates positive externalities by allowing for labor market pooling, input sharing, and knowledge spillovers. (Rosenthal & Strange 2004)

Accessibility and Land Value (+)

Accessibility and land value comprise a positive feedback system. Where land is expensive, it is developed more intensively. Where it is more intensively developed, there are more activities and destinations that can be reached in a given time. Where there are more activities, accessibility is higher. Where accessibility is higher, land is more expensive.

Gas tax and electric vehicle usage

Gas Tax and Electric Vehicle Usage (+) Imagine all gasoline vehicle users pay for all transportation costs. Imagine total expenses are $100,000,000 and the total number of users are 1,000,000, traveling 10,000 miles per year (for a total travel of 10,000,000,000 miles per year, at a cost of $0.01/mile), and all gasoline powered cars get 30 MPG. In that case, if all vehicles are gasoline powered, the gas tax will be $0.30/gallon (or $0.01/mile), in line with current costs. Now imagine, only half of all cars pay the gas tax, the tax jumps to $0.60 to cover costs, still quite tolerable, but as the gas tax rises, the number of gasoline powered cars should be expected to fall. The following image shows the expected gas tax based on the above assumptions with a varying number of gasoline powered cars on the road. Note especially this is a log-log scale. At 50,000 cars with gasoline engines (95% non-gasoline powered), the tax jumps to $6.00 per gallon (above European levels), but the last car has to pay $300,000 per gallon. The move away from the gas tax is a positive feedback system that will accelerate. A replacement may be required.

Urban Transit (The "Mohring Effect") (+) Fixed-route urban transit networks also have the potential to exhibit characteristics of a positive feedback system through a process known as the "Mohring effect". Since the costs facing users of public transit services include elements such as the user's time, which has a fixed component to account for time spent waiting for a bus or train, it can be shown that at higher levels of demand waiting times decrease due to more frequent service. This, in turn, makes public transit more attractive. Thus, the setting of marginal cost fares should take into account relevant user time costs in order to achieve optimality. The Mohring effect may provide an efficiency rationale for the subsidization of some urban transit services.

The Mohring effect may arise through the provision of more frequent service on a single route, as described above, and also in a network setting. For example, if the density of routes in a network are increased, the time costs faced by users in accessing the nearest stop will decrease, again reducing the total cost of a trip.

Mode Choice and the Mogridge hypothesis (+) (see Mogridge, M.J.H., D.J. Holden, J. Bird and G.C. Terzis, 1987, The Downs/Thomson Paradox and the Transportation Planning Process, International Journal of Transport Economics, 14(3): 283-311.)

Why did the automobile take-off? Because at all values of auto-mode share, the automobile has a faster travel speed than transit, even though the city might be better off as a whole (have an overall faster speed) if the congestion from autos was avoided altogether and everyone rode the bus. Mogridge and others have hypothesized that this is indeed how congested transportation systems work in the absence of charges for road access.

Is the left figure correct? Or does the second figure (right) more accurately reflect the empirical evidence? The best collection of evidence to date has been compiled in a review by Mogridge.

Network Externalities

The idea underlying network externalities is that a network is more valuable the more people (destinations) who are on (served by) it.

Examples of networks

Examples of networks from communications include:

• telegraph,
• telephone,
• fax,
• email,
• World Wide Web,
• automated teller machines, and
• the English language.

In transportation, networks examples include:

• railroads,
• highways,
• airports,
• shipping containers.

Examples of network externalities

Non-transportation examples of network externalities include

• the typewriter keyboard,
• electrical sockets,
• nuts and bolts,
• weights and measures (SI or the metric system)

and anything else that has been standardized.

Exercise Identify four technologies (related in some way to transportation) in which network externalities exist (that have inter-organizational standards). […]

Terms

Terms that are often used in describing network externalities:

• Lock-in
• Path Dependence
• Critical Mass
• Increasing Returns
• Agglomeration Economies
• Bandwagon effect
• "Metcalfe's Law": The value of a network increases with the square of the number of members.

Agglomeration Economies

The idea of agglomeration economies has been long considered in urban economics. Transportation of one form or another drives these agglomeration economies.

The spatial economics literature observes: Specialized and diversified cities co-exist. Larger cities tend to be more diversified. The distribution of city-sizes and specializations tend to be stable over time. City growth is related to specialization and diversity. Relocations are from diversified to specialized cities. Assumptions include: crowding, agents, labour mobility, (endogenous) self-organisation, path-dependency, systems of cities (policentricity).

The following are some quotes about agglomeration:

• “My purpose is to show that cities are primary economic organs” (Jacobs 1969, p.6).
• “Development is a process of continuously improving in a context that makes injecting improvisations feasible. Cities create that context. Nothing else does” (Jacobs 1984, p.155).
• “The city is not only the place where growth occurs, but also the engine of growth itself” (Duranton 2000, p.291-292).
• “Large cities have been and will continue to be an important source of economic growth” (Quigly 1998, p.137).
• “Agglomeration can be considered the territorial counterpart of economic growth” (Fujita and Thisse 2002, p.389).

Agglomeration, productivity and (urban) scale in a knowledge driven economy

• "City-regions are locomotives of the national economies within which they are situated, in that they are the sites of dense masses of interrelated economic activities that also typically have high levels of productivity by reason of their jointly-generated agglomeration economies and their innovative potentials " Scott and Storper, 2003

• "Metropolitan spaces are becoming, more and more, the adequate ecosystems of advanced technology and economy…. [T]he decrease of communication costs does not by itself lead to a spreading and diffusion of wealth and power; on the contrary, it entails their polarization." Veltz, 2005

The following table enumerates different types of scale (intra-firm) and agglomeration (inter-firm) scale economies.

Type of scale economy				Example
Internal			1. Pecuniary	Being able to purchase intermediate inputs at volume discounts
	Technological		2. Static technological	Falling average costs because of fixed costs of operating a plant
			3. Dynamic technological	Learning to operate a plant more efficiently over time
External or Agglomeration	Localization	Static	4. Shopping	Shoppers are attracted to places where there are many sellers
			5. Adam Smith Specialization	Outsourcing allows both the upstream input suppliers and downstream firms to profit from productivity gains because of specialization
			6. Marshall labor pooling	Workers with industry-specific skills are attracted to a location where there is a greater concentration.a
		Dynamic	7. Marshall-Arrow-Romer Learning-by-doing	Reductions in costs that arise from repeated and continuous production activity over time and which spill over between firms in the same place
	Urbanization	Static	8. Jane Jacobs innovation	The more that different things are done locally, the more opportunity there is for observing and adapting ideas from others
			9. Marshall labor pooling	Workers in an industry bring innovations to firms in other industries; similar to no. 6 above, but the benefit arises from the diversity of industries in one location.
			10. Adam Smith division of labor	Similar to no. 5 above, the main difference being that the division of labor is made possible by the existence of many different buying industries in the same place
		Dynamic	11. Romer endogenous growth.	The larger the market, the higher the profit; the more attractive the location to firms, the more jobs there are; the more labor pools there, the larger the market—and so on
			12. Pure agglomeration	Spreading fixed costs of infrastructure over more taxpayers; diseconomies arise from congestion and pollution

Source: World development report 2009: reshaping economic geography By World Bank , Adapted from Kilkenny 1998

Standardization and Coordination Externalities

Image of Calculator Keypad: 0, 1, 2, 3 increasing from bottom to top.

Image of Telephone Keypad: 1, 2, 3 increasing from top to bottom, with 0 at bottom.

A typical remote control for Cable TV in the first part of the 21st century has up and down arrows to adjust channels. Pushing the up (plus) button will move you away from channel 0, while the down button will move you toward channel 0 (although if you reach the final channel, you will return to home). But remote controls also have a navigation for the onscreen guide - these have an up, down, left, and right arrow. The up arrow moves you through the onscreen guide, but here up move you toward channel 0, while down moves you away from 0. The left and right arrows move you forward or backward through time.

These remote controls have a further set of controls to operate an auxiliary device like a DVD or an inbuilt device like a personal video recorder. The left arrow, following the convention from tape recorders, plays (forward in time), while the double left arrow (on the right-most side) is fast forward and the double right-pointing arrow (on the left side) moves you in reverse (rewind). Other buttons do other things.

Complaints about the complexity of modern remote controls are hardly unique . Each remote is custom for a particular box, so as people accumulate boxes attached to TVs, the number of remotes increases accordingly. The utopia of the universal remote remains unreached; one hopes the situation will not sustain for another few decades before standardization moves in, or some other interface becomes widespread.

Like remote controls, keypads are another area where conventions may confuse.

Keypads on telephones and calculators represent the same ten digits, however they have different layouts. The telephone keypad, introduced with the advent of Touch Tone dialing by the Bell System in the 1960s places 0 (or O for operator, it is not always clear on telephones) at the bottom, and then numbers digits 1 - 9 in three rows of three columns each from the top. A calculator keypad (also used on computer keyboards) on the other hand, while it places 0 at the bottom, numbers 1 to 9 also in three rows of three columns, but in this case beginning at the bottom, as shown in Figure. These conventions have carried over to computers, which could array numbers in any random way, but use the different conventions to represent the different devices. Newer devices, such as television remote controls, could use either, but typically follow the telephone layout (though some have original layouts themselves, e.g. going from 1 to 4 on the first row, 5 to 8 on the second row, and 9 and 0 on the third row).

For operating a television, rarely an urgent activity, the additional cognitive load of a poorly-designed or non-standard interface is annoying, but not dangerous. With the case of election ballots, such confusion and resulting error may change the outcomes (such as the odd butterfly ballot used in West Palm Beach, Florida in the 2000 Presidential election, resulting in a disproportionate (compared to other jurisdictions) number of votes for Pat Buchanan, and likely giving the state of Florida, and thus the United States electoral college and the presidency to George W. Bush).

American travelers trying to write emails in some European countries may note that the standard QWERTY keyboard found in the English speaking world (so-named for the keys on the top-row of letters) has been replaced by a keyboard, which mainly swaps the Y and Z, but has some minor changes, dubbed the QWERTZ kezboard. This is just enough to throw off touch-tzpists (er, typists). I am sure the confusion is two-way.

For driving cars in the United States, many functions have been fortunately standardized. The brake foot pedal is on the left, the accelerator on the right. The steering wheel itself usually performs as expected. Less critical functions remain confusing, especially when switching cars, or driving an unfamiliar vehicle, such as a rental car, the difficulty compounds as this is usually done in an unfamiliar place. Where is the windshield wiper? The light switch? The brights? The transmission control? The radio? The environmental controls? The locks? The window controls? The rear-view window control? The unlock for the trunk? The unlock for the gas tank? Where is the gas tank - driver or passenger side? All vary with make, model, and year of vehicle.

Driving on the left of the right is standardized locally, but not globally. As any traveler from continental Europe, North America, or South America knows, things differ on the islands of Great Britain, New Zealand, Japan, the Caribbean, and even the island-continent of Australia and the Indian subcontinent.

Traffic signals usually report red on top and green on bottom. What does it mean when the light is simultaneously red and green? Or red and yellow (amber), or green and yellow? Or the green light flashes? All of these patterns are local, but not global standards.

Construction of Revealed Demand (Fulfilled Expectation) Curve with Positive Network Externalities

Construction of Revealed Demand (Fulfilled Expectation) Curve with Positive Network Externalities

(based on Economides, Nicholas (1996) The Economics of Networks. Journal of Industrial Organization, Vol. 14, no. 6, pp. 673-699 October 1996)

A demand curve for a typical good is downward sloping, the more it costs, the less that will be consumed. However, the demand for a network good rises with the number of members of the network (Economides 1996). Each user of the network creates a positive externality for other users. Thus, networks exhibit a seemingly upward sloping demand curve, self-limiting at saturation, with perfectly inelastic demand.

Rationale

Figure 1 constructs the revealed demand curves for positive network externalities. Let $P(n;n_{e})$ be the willingness to pay for the nth unit of the good when n_e units are expected to be sold (assume each consumer purchases only one unit of the good). The network is more valuable the more units are sold. With only one consumer, ($n=1$), the network is not particularly valuable, so the implicit demand at $n=1$ ($D_{1}$) is low, lower than at $D_{2}$, which is lower than $D_{3}$, etc. Drawing a line between the number of consumers ($n$) and the implicit demand curve at that number ($D_{n}$) traces out an approximately parabolic shape, $P(n,n)$.

Conditions

$P(n,n)$ is the equilibrium price where the demand curve for a network of size $n$ ($D_{e}$) intersects the vertical projection of the network size when the number of consumers (network size) is $e$. $P(n,n)$ is thus the fulfilled expectations (or revealed demand) curve, the set of prices that the nth consumer would actually pay to join the network which would sustain n-consumers. The fulfilled expectations demand is increasing for small $n$ if any one of three conditions hold:

1. “The utility of every consumer in a network of zero size is zero, or
2. there are immediate and large external benefits to network expansion for very small networks, or
3. there is a significant density of high-willingness-to-pay consumers who are just indifferent on joining a network of approximately zero size.”

Saturation

While demand rises with the number of members, thereby exhibiting positive critical mass under perfect competition, there is a saturation point, such that increasing the number of members does not add value. Such a system exhibits multiple equilibria (the largest of which is stable), and under perfect competition, the amount of network may be under-supplied because the positive externalities cannot be internalized to the producing firms.

Intersection with U-shaped cost curves

A - supply intersects demand twice: when cost is decreasing and demand is increasing, and when cost is increasing and demand is decreasing

B - supply intersects demand twice: when cost is decreasing and demand is decreasing, and when cost is increasing and demand is decreasing

C - supply intersects demand twice: when cost is decreasing and demand is increasing, and when cost is increasing and demand is increasing

D - supply does not intersect demand

We might then think about intersecting our parabolic demand curve with our U-shaped supply curve. Ignoring tangencies, four key outcomes are possible, as shown in the figures below. In the three cases (A,B,C) where the curves intersect, the intersection on the right side, denoted Q*, would be a stable equilibrium. However, to get to the intersection on the right, one might have to pass through the intersection on the left.

Analogy between Scale and Scope economies on the cost side

In the chapter on costs we noted that there exist scale and scope economies on the cost side. Scale economies indicate it is cheaper to produce a given amount if more units are being produced (as a fixed cost can be spread over more units) and scope economies indicate it is cheaper to produce multiple goods together rather than separately.

On the demand side, we noted above network externalities, which are analogous to scale economies, it is more valuable to consume the more consumers there are. Goods may also be more valued if consumed together rather than separately (e.g. complements) or because variety is preferred to monotony. These Variety or Inter-technology externalities are analogous to economies of scope.

Other Concepts Related to Positive Feedback Systems

Companion-Innovation

(based on Garrison W, Souleyrette R, (1996), "Transportation, Innovation and Development: The Companion Innovation Hypothesis", Logistics and Transportation Review, vol. 32, pp. 5-38).

The economy is a series of linked markets. The "companion innovation" hypothesis suggests that improvements in transport energize other sectors of the economy.

Does the demand curve include those positive externalities?

How smart are markets?

Does willingness to pay change over time at a rate greater than the discount rate?

The reorganization and innovation lead to productivity growth, which should be captured from a macro-economic perspective (see the lecture on transportation and productivity). If positive externalities are not captured (and negative are), there is clearly underinvestment.

Learning Curves

Average variable costs decline with output and time as processes get more efficient (people get smarter). Research and Development is a function of market size, which helps explain the process.

Consumption Economies

Average fixed costs decline with market size.

In markets with large fixed costs that have cost recovery as an aim (public infrastructure as an example), this can be very important. As the market grows, the cost per user drops. This of itself should increase demand – and can be seen as a positive consumption scale externality

S-Curves and Linked S-Curves

Increasing and Decreasing Returns and Equilibrium

(see Arthur, Brian (1990) Increasing Returns and Path Dependence in the Economy. The University of Michigan Press.)

How Networks Grow

To start, a network must have value to some network members at a minimal size (exceeding the cost of joining), or it must be subsidized. Success conditions for a new network suggest

1. it must either be compatible with existing networks (i.e. not really so new), or
2. be significantly more valuable to get people to adopt it.

For instance, the interstate highways were compatible with the existing vehicle highway system, interchanges were built, and the same cars could use both. Railroads on the other hand were very valuable compared with canals and animal led carts against which they were initially competing, enabling their success despite the incompatibility of the technologies. In short, if compatibility has costs, it can limit the market because of the extra handling costs, additional waiting time, or an additional layer of processing (such as software) required to decode things.

Thomas Hughes said "Mature systems suffocate nascent ones". This means that well-developed technologies occupying a particular niche make it very hard for a new technology to move into that niche, since it does not have all of the compatible infrastructure and correlated compatible technologies.

Where Does Intelligence Lie

• Smart Networks, Dumb Packets/Vehicles (Railroads, Telephone)
• Smart Packets/Vehicles, Dumb Networks (Roads, Internet)

Important to resolve this in network design

Network Design vs. Network Growth

Network Design Problem (NDP) tries to determine “optimal” network according to some criteria (Z). - Normative

E.g. Maximize Z, subject to some constraints.

Network Growth Problem tries to predict actual network according to observed or hypothesized behaviors. - Positive

Questions

• Why do networks expand and contract?
• Do networks self-organize into hierarchies?
• Are roads an emergent property?
• Can investment rules predict location of network expansions and contractions?
• How can this improved knowledge help in planning transportation networks?
• To what extent do changes in travel demand, population, income and demographic drive changes in supply?
• Can we model and predict the spatially specific decisions on infrastructure improvements?

Network Growth

• Depends on existing and forecast transportation demand
• Depends on existing transportation supply
• Network can be viewed as output of a production function: N = f( D, S)

Over the long term, we expect networks to grow in the fashion of an S-Curve as discussed in the Lesson on Positive Externalities

How networks change with time

• Nodes: Added, Deleted, Expanded, Contracted
• Links: Added, Deleted, Expanded, Contracted
• Flows: Increase, Decrease

The Node Formation Problem

• Christaller’s Central Place Theory (CPT) sought to answer: How are urban settlements spaced, more specifically, what rules determine the size, number and distribution of towns? Christaller’s model made a number of idealizing assumptions, especially regarding the ubiquity of transport services, in essence, assuming the network problem away. His world was a largely undifferentiated plain (purchasing power was spread equally in all directions), with central places (market towns) that served local needs. The plain was demarcated with a series of hexagons (which approximated circles without gaps or overlaps), the center of which would be a central place. However some central places were more important than others because those central places had more activities. Some activities (goods and services) would be located nearer consumers, and have small market areas (for example a convenience store) others would have larger market areas to achieve economies of scale (such as warehouses).

Central Place & Network Hierarchy

Network Hierarchy is much like Central Places (Downtown Minneapolis, Suburban Activity Centers (e.g. Bloomington, Edina, Eden Prairie), Local Activity Centers (e.g. Dinkytown, Stadium Village, Midway), Neighborhood Centers (4th Avenue & 8th Street SE).

Central Places occur both within and between cities. Hierarchy: Minneapolis-St. Paul; Duluth, St. Cloud, Rochester; Morris, Brainerd, Marshall, etc.; International Falls, etc.

Exercise

• Use SONG Model to understand network growth. Go to:SONG Homework Assignment

Further reading

• Levinson, David and Ramachandra Karamalaputi (2003) Predicting the Construction of New Highway Links. Journal of Transportation and Statistics. Vol. 6(2/3) 81-89.
• Levinson, David and Ramachandra Karamalaputi (2003) Induced Supply: A Model of Highway Network Expansion at the Microscopic Level. Journal of Transport Economics and Policy, Volume 37, Part 3, September 2003, pp. 297–318.

Thought Question: Applications of Positive Externalities

• Do Positive Externalities Exist (or are they Internalized?) Discuss …
• What does this say for the prospects of Intelligent Transportation Systems?
• What are the prospects for Automated Highway Systems as opposed to Intelligent Vehicles (and relatively Dumb Roads)?

Other Resources

Other Resources in Transportation Economics

Committees

• Transportation Research Board Transportation Economics Committee
• Benefit Cost Analysis wiki of TRB Transportation Economics Committee

Journals

• Journal of Transport Economics and Policy current issues (not free)
• Journal of Transport Economics and Policy archives (1967-2000) (free)
• International Journal of Transport Economics (not free)
• Elsevier's Research in Transport Economics (not free)

Reports

• Facts and Furphies in Benefit-Cost Analysis: Transport