<p>Intuitively, this just says that if the bundle you choose was possible under wealth <span class="math-container">$w$</span> and price <span class="math-container">$p$</span> but it is not <span class="math-container">$x(p, w)$</span>, then it must be that you cannot obtain it when price is <span class="math-container">$p'$</span> and wealth is <span class="math-container">$w'$</span>.</p>

<p>It simply does not say anything about case (b) in which <span class="math-container">$p' \cdot x(p'', w'') &gt; w$</span> and <span class="math-container">$p'' \cdot x(p', w') &gt; w''$</span>. Since the first part of the if ... then statement in the definition is false, everything evaluates to true.</p>

CC BY-SA 4.0
2019-11-07T13:22:30.850Z
Thanks for the answer, and I can get the intuition of what WARP says. Just to clarify, by "Since the first part of the if ... then statement in the definition is false, everything evaluates to true.", do you mean Definition 2.F.1 of MWG is incorrect?
Yun
CC BY-SA 4.0
2019-11-08T01:36:27.647Z
The definition is correct. Let's say the definition is "a demand function satisfies WARP if ($x$ and $y$ then $z$)". I was just saying that figure (b) also fits into the definition since $x$ (in figure (b)) is false, so the hole thing evaluates to true.
Art
CC BY-SA 4.0
2019-11-07T09:08:02.687Z
2019-11-07T09:08:02.687Z
Art
<p>I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). 
<a href="https://i.sstatic.net/KjzlE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/KjzlE.png" alt="enter image description here"></a>
<a href="https://i.sstatic.net/LWPDI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LWPDI.png" alt="enter image description here"></a>
However, as the choice <span class="math-container">$x(p',w')$</span> is only feasible under the price-income level <span class="math-container">$(p',w')$</span> and <span class="math-container">$x(p'',w'')$</span> is only feasible under <span class="math-container">$(p'',w'')$</span> in Figure 2.F.1(b), why does it still satisfy the WARP definition which requires that a choice (say, <span class="math-container">$x(p',w')$</span>) should be feasible under two different price-income levels (say, <span class="math-container">$(p',w')$</span> and <span class="math-container">$(p'',w'')$</span>)?</p>

<preferences><choice-theory><mwg>
Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?
Yun
# Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

(Asked by: username_0 on 2019-11-07)

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30).
[![enter image description here](https://i.sstatic.net/KjzlE.png)](https://i.sstatic.net/KjzlE.png)
[![enter image description here](https://i.sstatic.net/LWPDI.png)](https://i.sstatic.net/LWPDI.png)
However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is only feasible under $(p'',w'')$ in Figure 2.F.1(b), why does it still satisfy the WARP definition which requires that a choice (say, $x(p',w')$) should be feasible under two different price-income levels (say, $(p',w')$ and $(p'',w'')$)?

**Tags:** preferences, choice-theory, mwg

---

## 1 answers

### Answer by username_1 on 2019-11-07. Score: 4

Intuitively, this just says that if the bundle you choose was possible under wealth $w$ and price $p$ but it is not $x(p, w)$, then it must be that you cannot obtain it when price is $p'$ and wealth is $w'$.

It simply does not say anything about case (b) in which $p' \cdot x(p'', w'') > w$ and $p'' \cdot x(p', w') > w''$. Since the first part of the if ... then statement in the definition is false, everything evaluates to true.

> **Comments:**
> **username_0**: Thanks for the answer, and I can get the intuition of what WARP says. Just to clarify, by "Since the first part of the if ... then statement in the definition is false, everything evaluates to true.", do you mean Definition 2.F.1 of MWG is incorrect?  
> **username_1**: The definition is correct. Let's say the definition is "a demand function satisfies WARP if ($x$ and $y$ then $z$)". I was just saying that figure (b) also fits into the definition since $x$ (in figure (b)) is false, so the hole thing evaluates to true.  

---

