Questions tagged [elasticity-of-substituion]
The elasticity-of-substituion tag has no usage guidance.
31
questions
0
votes
0answers
38 views
Capital in terms of labor
I have a question that asks to find $\frac{\partial K}{\partial L} $
from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
0
votes
0answers
9 views
Can there be elasticity for income in an inferior good, when the price is out of its limits?
(Skip to 3. for the actual problem I am facing. Everything else is just to help you understand it better up to that point)
Two goods $X$ and $Y$ are substitutionals. For $P_X=20$ consumers ask for $Q_{...
0
votes
1answer
45 views
Calculating price elasticity by asking a “this” or “that” question
Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example)
If I decrease the price of both goods by 10% and ask:
"Do you prefer A for 9 or B for 18 "
What sort of insights (...
0
votes
0answers
14 views
Elasticity of substitution of a general production function with labor-augmenting technological progress
I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
2
votes
1answer
88 views
Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress
I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
1
vote
0answers
35 views
Negative elasticity of substitution in a CES production function
I have empirically estimated the elasticity of substitution parameter in the following model:
$$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho} $$
here, $Y_t$ is output, $A_i$ is a ...
0
votes
0answers
19 views
Elasticity of substitution, marginal rate of substitution and price ratio
so there is a problem I do not know how to tackle:
The is an utility maximisation problem and the solution to the Lagrangian leads to:$$\frac{C_1}{C_2}=(1+\rho)^\frac{1}{\sigma}(\frac{P_1}{P_2})^\...
0
votes
1answer
56 views
How to find the elasticity of substitution for the general CES-function?
I have to find the EOS for the general CES-function defined as
$$
y = (a_1x_1^p+a_2x_2^p)^{1/p}
$$
I first find $MP_1$ and $MP_2$ to find $MRTS$. We have that
$MP_1 = \frac{\partial y} {\partial ...
1
vote
0answers
74 views
Constant Elasticity of Substitution- profit maximization vs cost minimization
Consider the following production function:
$$
Y=A\left[\alpha K^{\rho}+\left(1-\alpha\right)L^{\rho}\right]^{\frac{1}{\rho}}
$$
In the above, $\rho$ is the substitution parameter, and $\sigma=\frac{1}...
1
vote
0answers
58 views
Elasticity of substitution
So, this is an economics question but the problem I have is a pure math problem I guess. So I have the following equation:f(x,y)
this function have the elasticity of substitution(EOS): 1/(1-beta). a,...
1
vote
0answers
14 views
How to simulate changes in quantity demanded when several prices change?
I am not sure if this is a straightforward question or not. Basically, I have a set of products along with their prices and quantities demanded. I also have own and cross price elasticities for each ...
1
vote
2answers
286 views
If $X$ is a Giffen good then $Y$ must be a normal good
While going through some problems as part of self-study I encountered the following True/False question:
Q. Steven only consumes two goods: $X$ and $Y$. If $X$ is a Giffen good for Steven, then $Y$ ...
2
votes
0answers
60 views
Relationship between Elasticity of substitution of sectoral outputs and elasticity of substitution of inputs
There are two sectors Y1 and Y2.
Composite output is given by CES form -
Each sector employs Capital and Labor in combination through Cobb-Douglas Production Technology.
The paper mentions that ...
6
votes
1answer
109 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
votes
1answer
73 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
votes
1answer
131 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}}...
1
vote
0answers
73 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} & ...
3
votes
0answers
131 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 $...
1
vote
0answers
74 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 ...
1
vote
0answers
23 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 ...
2
votes
0answers
105 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
votes
1answer
43 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
votes
1answer
259 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
votes
1answer
106 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:
$$\sigma = -\frac{d \ln (\frac{x_2}{x_1})}{d \ln(\frac{x_1}{1+x_2})}...
4
votes
1answer
362 views
Complementarity in CES Production Function
I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$),...
3
votes
2answers
140 views
Is optimal labour zero when (i) capital fixed and (ii) elasticity of substitution less than 1?
I am getting some "weird results". I find that in a CES, with short term fixed capital and elasticity of substitution smaller than one, it is optimal for firms to hire zero labour, which seems at odd ...
-2
votes
2answers
246 views
How do find elasticity of substitution for this function
The motive of my post is in search of some help in order to understand the correct way to find the elasticity of substitution by means of calculating the following function.
$$f(K, L)=\frac{K^{2}L^{...
1
vote
0answers
94 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{\...
1
vote
0answers
203 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 ...
3
votes
1answer
202 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 ...
5
votes
1answer
554 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 ...
