<p>If a good is inferior the Marshallian demand function will be steeper than the Hiсksian demand funсtion (it may even slope upwards if it is a Giffen good), this result comes directly from applying the definition of an inferior good to the Slutsky equation. Thus, the intersection of <span class="math-container">$h_1^1$</span> and <span class="math-container">$P_1^0$</span> will be to the right of <span class="math-container">$x_1^0$</span>, while the intersection of <span class="math-container">$h_1^0$</span> and <span class="math-container">$P_1^1$</span> will be to the left of <span class="math-container">$x_1^1$</span>. Thus, <span class="math-container">$h_1^0$</span> will be to the left of <span class="math-container">$h_1^1$</span> and they won't intersect. Hence, <span class="math-container">$EV &gt; CS &gt; CV$</span>.</p>

CC BY-SA 4.0
2021-12-28T17:00:07.773Z
2021-12-28T17:56:36.143Z
2021-12-28T17:56:36.143Z
LudwigNagasena
<p>I've seen this intuitive graphical proof of why EV &lt; CS &lt; CV for normal goods which interprets the integrals as areas under the respective curves (see below). Can you also do this for inferior goods to show EV &gt; CS &gt; CV?</p>
<p><a href="https://i.sstatic.net/9KZhs.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9KZhs.png" alt="enter image description here" /></a></p>

<microeconomics>
Graphical proof of CV, CS, EV comparison for inferior goods
user39999
# Graphical proof of CV, CS, EV comparison for inferior goods

(Asked by: username_0 on 2021-12-27)

I've seen this intuitive graphical proof of why EV < CS < CV for normal goods which interprets the integrals as areas under the respective curves (see below). Can you also do this for inferior goods to show EV > CS > CV?

[![enter image description here](https://i.sstatic.net/9KZhs.png)](https://i.sstatic.net/9KZhs.png)

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2021-12-28. Score: 0 | Accepted answer

If a good is inferior the Marshallian demand function will be steeper than the Hiсksian demand funсtion (it may even slope upwards if it is a Giffen good), this result comes directly from applying the definition of an inferior good to the Slutsky equation. Thus, the intersection of $h\_1^1$ and $P\_1^0$ will be to the right of $x\_1^0$, while the intersection of $h\_1^0$ and $P\_1^1$ will be to the left of $x\_1^1$. Thus, $h\_1^0$ will be to the left of $h\_1^1$ and they won't intersect. Hence, $EV > CS > CV$.


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