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6 votes

Cost function from CES production function

If you are interested in the case where $\rho \geq 1$ then look at the post CES $\ \ \rho \geq 1$. For the standard case where $0 < \rho < 1$ you should get a result like this $$C(w_1,w_2,y) = \...
Jesper Hybel's user avatar
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3 votes
Accepted

FOCs for the Dixit-Stiglitz aggregator: derivative of an integral w.r.t. integrand at one point

The `heuristic' way of taking first order conditions is indeed a bit 'mathematically' dodgy. For this type of problems, where you are maximizing over an entire function, the first order conditions are ...
tdm's user avatar
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3 votes
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The Intuition of CES Utility

This is going to be a long answer, and I'm not completely sure if it is going to answer your questions as I'm mostly going to focus on the derivations of the own and cross price elasticities. Most of ...
tdm's user avatar
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2 votes
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Showing that the CES is non-decreasing in the elasticity of substitution

Ok, thanks to Giskard, I found the proof: I think it is so elegant it deserves to be shared. Let's take $$ U(x_1, ..., x_L) = \left( \sum_{l=1}^{L}\alpha_l x_l^{\rho} \right)^{1/\rho} $$ With $\rho = \...
Matteo Bulgarelli's user avatar
2 votes
Accepted

Marshall demand for simple CES utility

To answer this question I will first generalize slightly the question to deal with the utility function $$u(x) = \left(\sum_j x_j^\alpha\right)^{1/\alpha}$$ The Marshall demand can be written as $$x_k^...
Jesper Hybel's user avatar
  • 3,531
2 votes

Is CES production representing the average of inputs?

Yes, all this does mean that the production function represents the average of two inputs $L$ and $K$ for different values of $\alpha$, given that $0<\gamma<1$. The key thing to consider here is ...
Pallak Goyal's user avatar
1 vote

Are homothetic additively separable preferences always equivalent to CES?

The second to top "Related" question (What utility functions are equivalent to additive functions?) contained a link to Ted Bergstrom's Lecture Notes on Separable Preferences, which answered ...
cfp's user avatar
  • 252

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