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

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This is my solution:

enter image description here

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?

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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 $v(\alpha p_1, \alpha p_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p_1p_2}$

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    $\begingroup$ Thanks! I asked the professor about it and he realized that he made a mistake there. $\endgroup$ – mn2609 Jul 13 at 18:25

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