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I'm trying to solve problem 5.13 from Nicholson and Snyder's Microeconomic Theory. The problem is about the so-called AIDS function in economics, which is the logarithm of the expenditure function. In the two goods case, this function (confirmed with the Solutions) is

$ln(E)=[...]+U\beta_{0}p_1^{\beta_{1}}p_2^{\beta_{2}}$

(the first part of the function is irrelevant).

Part c) of the problem asks to give $\frac{d \ln(E)}{d \ln(p_1)}$. I substituted $p_1=e^{ln(p_1)}$. The derivation gave me

$[...]+U\beta_{0}\beta_{1}p_1^{\beta_{1}}p_2^{\beta_{2}}$

(Again, I left out the first part of the equation as it is correct according to the solutions).

However, the solutions state that the final part of the answer is $U\beta_{0}\beta_{1}p_1^{\mathbf{\beta_1-1}}p_2^{\beta_{2}}$ instead of $U\beta_{0}\beta_{1}p_1^{\beta_{1}}p_2^{\beta_{2}}$. Where does the $-1$ come from? I suspect there might be a typo in the solutions.

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    Don't you mean part c) asks you to find the expression below? $$ \frac{d \ln E}{d \ln p_1} $$ If so, I agree with your derivation. – 2017-02-05
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    Indeed, that's what I meant. – 2017-02-05
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    You should edit your question to reflect that. I suspect there is a typo in your solutions. – 2017-02-05

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