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2 votes

Is cross-price elasticity a Cobb-Douglas production function?

As stated in the comments, there is no economic connection between a demand function and a production function. The only connection between the two functional forms is that both of them are log-linear....
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0 votes

Cobb-Douglas utility function. Deriving the price index with N discrete goods functions

It is going to be easier to use the log form for the Cobb-Douglas: $\ln(u) = \sum_i \alpha_i \ln(q_i)$. We can also assume that $\sum_j \alpha_j = 1$. The expenditure function is given by: $$ \min_{q} ...
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1 vote

Cobb-Douglas utility function

They don't have to, look: $U(x,y) = x^2y^2$ is Cobb-Douglas type, but the exponents sum up to four. It is also true that $U()$ represents the same preferences as $\hat{U}(x,y) = \sqrt{xy}$, where the ...
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4 votes

Confusion on deriving Walrasian price changes using IFT

First, there is a slight mistake in your first order condition as $x_2$ needs to be in the numerator and $x_1$ in the denominator. The two first order conditions can be written as: $$ \alpha p_2 x_2 - ...
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