<p>&quot;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&quot;.</p>
<p>In other words, the Weak Axiom of Revealed Preference (WARP) refers to consistent (rational) decision-making.</p>
<p>I think the proof is in terms of an 'if then' direct method:</p>
<p>The Marshallian demand function <span class="math-container">$x(p,w)$</span> satisfies WARP if the following property holds for any two price-wealth situations <span class="math-container">$(p,w)$</span> and <span class="math-container">$(p',w')$</span>.</p>
<p>If <span class="math-container">$p*x(p',w')\leq w$</span> and <span class="math-container">$x(p,w)\neq x(p',w')$</span> then: <span class="math-container">$p'*x(p,w)&gt;w'$</span>.</p>

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2020-11-22T19:31:32.940Z
2020-11-23T13:52:33.050Z
2020-11-23T13:52:33.050Z
EB3112
<p>This question is from MWG</p>
<p>if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom.</p>
<p>I cannot prove this statement. How can I do?Thanks alot.</p>

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2020-11-22T19:29:10.807Z
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.
Bayesian
<microeconomics><consumer-theory><preferences><self-study><mwg>
A question from MWG 2F12
studentp
# A question from MWG 2F12

(Asked by: username_0 on 2020-11-22)

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.

**Tags:** microeconomics, consumer-theory, preferences, self-study, mwg
> **Comments:**
> **username_1**: 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.  

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## 1 answers

### Answer by username_2 on 2020-11-22. Score: 3 | Accepted answer

"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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