Advanced Microeconomics/Revealed Preferences

Weak Axiom of Revealed Preferences

The demand function $x(p,w)$ satisfies the weak axiom of revealed preference if:
$\forall (p,w),(p^{\prime },w^{\prime }){\mbox{ if }}px(p^{\prime },w^{\prime })\leq w{\mbox{ and }}x(p^{\prime },w^{\prime })\neq x({p},{w}){\mbox{ then }}p^{\prime }x({p},{w})>w^{\prime }$

In words:
The consumer faced with $(p,w)$ could have chosen $\funcd{x}{p^{\prime},w^{\prime}}$ but chose $x(p,w)$, assuming the consumer chooses consistently, if $\funcd{x}{p^{\prime},\primd{w}}$ is ever chosen, $x(p,w)$ must not be affordable. Hence, $p^{\prime }\cdot x(p,w)>w^{\prime }$