Advanced Microeconomics/Revealed Preferences

Weak Axiom of Revealed Preferences

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

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