# Tag Info

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 $$C(w_1,w_2,y) = \... • 3,531 3 votes Accepted ### FOCs for the Dixit-Stiglitz aggregator: derivative of an integral w.r.t. integrand at one point The `heuristic' way of taking first order conditions is indeed a bit 'mathematically' dodgy. For this type of problems, where you are maximizing over an entire function, the first order conditions are ... • 12.5k 3 votes Accepted ### The Intuition of CES Utility This is going to be a long answer, and I'm not completely sure if it is going to answer your questions as I'm mostly going to focus on the derivations of the own and cross price elasticities. Most of ... • 12.5k 2 votes Accepted ### Showing that the CES is non-decreasing in the elasticity of substitution Ok, thanks to Giskard, I found the proof: I think it is so elegant it deserves to be shared. Let's take$$ U(x_1, ..., x_L) = \left( \sum_{l=1}^{L}\alpha_l x_l^{\rho} \right)^{1/\rho} $$With \rho = \... 2 votes Accepted ### Marshall demand for simple CES utility To answer this question I will first generalize slightly the question to deal with the utility function$$u(x) = \left(\sum_j x_j^\alpha\right)^{1/\alpha}$$The Marshall demand can be written as$$x_k^...
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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 ...