# Advanced Microeconomics/Revealed Preferences

Jump to: navigation, search

### Weak Axiom of Revealed Preferences

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

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, $p^{\prime}\cdot x(p,w) > w^{\prime}$