<p>There is no error in your calculations. The problem is with the indirect utility function that you were given. </p>

<p>An indirect utility function should satisfy <span class="math-container">$v(\alpha p_1,\alpha p_2,\alpha y)=v(p_1,p_2,y)$</span>. In other words, if income goes up and prices go up by the same factor then everyone is as well off as they were before.</p>

<p>Unfortunately, in this case <span class="math-container">$v(\alpha p_1, \alpha p_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p_1p_2}$</span></p>

CC BY-SA 4.0
2019-07-13T18:25:12.167Z
Thanks! I asked the professor about it and he realized that he made a mistake there.
mn2609
CC BY-SA 4.0
2019-07-12T17:47:21.080Z
2019-07-12T17:47:21.080Z
Angela Pretorius
<p>in preparation for our upcoming exam, our tutor has uploaded sample questions. One of them is the following:</p>

<p><a href="https://i.sstatic.net/T9Cs5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/T9Cs5.png" alt="enter image description here"></a></p>

<p>This is my solution:</p>

<p><a href="https://i.sstatic.net/MXZKM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/MXZKM.png" alt="enter image description here"></a></p>

<p>Which differs from the solution, which gives the ordinary square root of the same parameters, not the 4th-one. I can't find my mistake, does anyone have any ideas?</p>

<microeconomics>
Transforming an indirect utility function into an expenditure function
mn2609
# Transforming an indirect utility function into an expenditure function

(Asked by: username_0 on 2019-07-09)

in preparation for our upcoming exam, our tutor has uploaded sample questions. One of them is the following:

[![enter image description here](https://i.sstatic.net/T9Cs5.png)](https://i.sstatic.net/T9Cs5.png)

This is my solution:

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

Which differs from the solution, which gives the ordinary square root of the same parameters, not the 4th-one. I can't find my mistake, does anyone have any ideas?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2019-07-12. Score: 2

There is no error in your calculations. The problem is with the indirect utility function that you were given.

An indirect utility function should satisfy $v(\alpha p\_1,\alpha p\_2,\alpha y)=v(p\_1,p\_2,y)$. In other words, if income goes up and prices go up by the same factor then everyone is as well off as they were before.

Unfortunately, in this case $v(\alpha p\_1, \alpha p\_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p\_1p\_2}$

> **Comments:**
> **username_0**: Thanks! I asked the professor about it and he realized that he made a mistake there.  

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