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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"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: $p'*x(p,w)>w'$.