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Questions tagged [elasticity-of-substituion]

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Elasticity of substitution between leisure in two periods

This is a basic question, but I am new to macro models. The question is from Romer's text. Assume a household only has one member and has no initial wealth, and the household lives for two periods. ...
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Second order partial derivative and cross second-order partial derivative

I'm following a paper (Full text available here!) where at some point (pag.17 and 20) the author get the following derivative: $$\frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}...
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Demand Elasticity, Factor Substitution: Independent?

Given $ Y=f(K,L;\sigma) $, the effect on labor from a change in the price of capital can be gauged through a substitution effect and a scale effect: \begin{align*} \frac{\partial L}{\partial r} & ...
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Wages, capital: Substitution and Output Effects

Consider a CES production function $Y=f(K,L)$ with elasticity of factor substitution $\sigma>0$. The substitution effect of higher real wages naturally implies a shift along the isoquant to more $...
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Elasticity of substitution meaning

If I computed an elasticity of substitution of f.e. 0.9 between capital and labour, does this implicate that the factors are rather well substitutable or not? Since for 0 they are perfect complements ...
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Raising the elasticity of substitution in an economy

Papers such as de la Grandville (1989) and Klump/de la Grandville (2000) have shown that a higher elasticity of substitution leads to higher economic growth. My question is, if there is a way to ...
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Elasticity of substitution of a CES production function [duplicate]

Given the CES-production function $y=(a_1x_1^p+a_2x_2^p)^\frac{1}{p}$, where $a_1\neq a_2$. (a) Find the elasticity of substitution of the function. I'm really uncertain if I'm doing this correctly, ...
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Constant elasticity of substitution utility function to Cobb-Douglas [duplicate]

How to prove that constant elasticity of substitution utility function $u=(\frac{1}{\mid{M}\mid} \int_{i\in M}q(i)^{\frac{\sigma-1}{\sigma}}di)^{\frac{\sigma-1}{\sigma}}$ is the same as Cobb-Douglas ...
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Elasticity of Substitution and Taxation

So I am trying to understand the impact of the elasticity of substitution in terms of taxation. I am carrying this out for the U.S. by firstly estimating a two-input CES production function. Chirinko (...
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Linearization of VES production funtions

I know that the linearization of a CES (constant elasticity of substitution) funtion is a bit complicated. There is even an R package dedicated just for that - the econometric estimation and ...
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1answer
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Empirical measurements of consumption and production elasticity of substitution?

The consumption elasticity of substitution (ES) is the ES between different consumption goods. The production ES is the ES between factors of production. My question is: are there any serious ...
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1answer
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CES production function application problem

I'm currently trying to do some estimations using the micEconCES package in R by Henningsen/Henningsen (2011). My issue is that I am not very familiar with R and I'm trying to implement my own dataset ...
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Estimating a constant elasticity of substitution (CES) production function

I'm currently on my paper about estimating a CES function for the USA. I use a regular two input function with capital and labour. I would then use nonlinear estimation methods aswell as the kmenta ...
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1answer
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Interpretation: Elasticitity of Substitution [closed]

I have this production function: $$P(x_1,x_2)=x_1+x_1*x_2$$ I am trying to find the elasticity of substitution, and I found this: $$\sigma = -\frac{d \ln (\frac{x_2}{x_1})}{d \ln(\frac{x_1}{1+x_2})}...
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1answer
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Complementarity in CES Production Function

I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$),...
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2answers
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Is optimal labour zero when (i) capital fixed and (ii) elasticity of substitution less than 1?

I am getting some "weird results". I find that in a CES, with short term fixed capital and elasticity of substitution smaller than one, it is optimal for firms to hire zero labour, which seems at odd ...
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2answers
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How do find elasticity of substitution for this function

The motive of my post is in search of some help in order to understand the correct way to find the elasticity of substitution by means of calculating the following function. $$f(K, L)=\frac{K^{2}L^{...
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CES utility in dynamic setting

Suppose I have a multiperiod consumption-saving problem with two or multiple goods able to be consumed. If the utility within a period is Constant Elasticity of Substitution, ie. $C = (c_1^\frac{\...
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How does one derive the elasticity of substitution with implicit functions?

I would like to derive the elasticity of substitution. I'm aware that such a thread with a very straightforward explanation already exists, but my case is slightly different and I'm not sure how to ...
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1answer
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Obj function yielding independent goods demand functions

I know that if the objective function (aka utility) is homothetic, demand functions will be linear in income. So for an homothetic demand function to give goods independent of prices other than their ...
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Estimating elasticity of substitution in nested CES functions

I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following ...