Advanced Microeconomics/Revealed Preferences

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Weak Axiom of Revealed Preferences[edit]

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}