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Questions tagged [elasticity-of-substituion]

6
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1answer
56 views

Econ Intuition for Jacobian inverse in demand system

Consider the following simple linear demand system (in vector notation) with n different products Demand: $\quad\mathbf{q=B\left(a-P\right)}$ Inverse demand: $\quad\mathbf{p=a-B^{-1}q}$ where $\...
0
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1answer
38 views

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. ...
0
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1answer
42 views

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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0answers
60 views

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} & ...
2
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1answer
86 views

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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0answers
35 views

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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0answers
19 views

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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0answers
53 views

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 ...
2
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1answer
34 views

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 ...
2
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1answer
208 views

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 ...
0
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1answer
85 views

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})}...
4
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1answer
227 views

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 ($I_{b,t}$),...
4
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2answers
127 views

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
157 views

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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0answers
71 views

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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0answers
161 views

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 ...
4
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1answer
149 views

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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411 views

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 ...