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This question is from MWG

if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom.

I cannot prove this statement. How can I do?Thanks alot.

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    $\begingroup$ Usually, homework questions are not allowed here. For graduate books like MWG, I am willing to turn a blind eye. However, at least (i) write down the question (and used definitions) properly such that people without the book can follow, and (ii) state why your own approach was not successful in answering the question. $\endgroup$ – Bayesian Nov 22 '20 at 19:29
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"If the new bundle was affordable at old prices, and the new and old bundles aren't equal, then the old bundle must not be affordable at the new prices".

In other words, the Weak Axiom of Revealed Preference (WARP) refers to consistent (rational) decision-making.

I think the proof is in terms of an 'if then' direct method:

The Marshallian demand function $x(p,w)$ satisfies WARP if the following property holds for any two price-wealth situations $(p,w)$ and $(p',w')$.

If $p*x(p',w')\leq w$ and $x(p,w)\neq x(p',w')$ then: $p'*x(p,w)>w'$.

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