Questions tagged [ces]

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Final demand for CES nested in Cobb-Douglas production function

I am deriving the final demand for intermediate good $x_j$ for the following final producer's problem: \begin{equation} \max_{{ k_{t}, x_{j,t}}} K^{1-\alpha}X^\alpha - R_tK_t - \int_{0}^{N_t}p_{j,...
Ciz1997's user avatar
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1 answer
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Are homothetic additively separable preferences always equivalent to CES?

Are homothetic additively separable preferences always a monotonic transformation of CES preferences? In technical language, the question is the following: Let $n>1$, and let $f:\mathbb{R}^n_{\ge 0}...
cfp's user avatar
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CES price index with heterogeneous productivity

When there is a distribution of productivity, so that different firms have different sale shares, the aggregate CES price index has shares as weights? References to papers are welcomed.
Luca Gi's user avatar
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2 answers
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Showing that the CES is non-decreasing in the elasticity of substitution

Is this possible? I've been trying so many times, without success, yet if I plot a two good CES on Wolfram, this seems true... I can't find a single numerical example where this does not hold, but I ...
Matteo Bulgarelli's user avatar
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150 views

How to get from a CES production function with inverse elasticity on weights to the special cases Cobb-Douglas & Leontief

I am dealing with a CES production function, and I have attempted some of the "traditional" ways to derive the Cobb-Douglas (logs & l'Hôpital) but I am not sure how to deal with the ...
user862800's user avatar
1 vote
0 answers
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on nested CES--derivation issue

I am reading Sachs and Kotlikoff (2012 NBER) and am wondering how they derive one equation in their paper. The setting is the following: Their model is a variant of the standard two-period ...
embeconp's user avatar
3 votes
1 answer
385 views

The Intuition of CES Utility

Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$ 1 The indirect ...
Alalalalaki's user avatar
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1 vote
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Derivation of wage rate from nested CES production function

could anyone please help to explain how equation (4) in this paper is derived? I understand that it's an application of first order conditions using the chain rule from equations (1)-(3), but the ...
wui's user avatar
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3 votes
0 answers
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An Extension to CES Demand

I am reading a paper with an extended CES final good setting: The representative household consists of a continuum of members, indexed by $k$ $C_{t}=\int C_{k, t} d k$ $C_{k, t}=\left(\int_{j \in \...
Alalalalaki's user avatar
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2 votes
1 answer
3k views

Cost function from CES production function

How can I find the cost function $c(w,p)$ given that the production is $$ f(x)=(x_1^p + x_2^p)^{1/p} \ \ for\ \ 0<p <1 $$ I tried to solve it and found that $$TC(y) = \left\{ \begin{...
victor's user avatar
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1 answer
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Marshall demand for simple CES utility

Assume that preferences are given by a utility function is given $$u(x_1,x_2) = (x_1^\rho + x_2^\rho)^{1/\rho}$$ what then are the Marshall demand given budget constraint $$p_1x_1 + p_2x_2 \leq I$$
Jesper Hybel's user avatar
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