Questions tagged [elasticity-of-substituion]
The elasticity-of-substituion tag has no usage guidance.
41
questions
5
votes
1answer
106 views
Derive and Decompose The Aggregate Elasticity of Substitution in CES Economy
The paper is Oberfield & Raval 2021.
Consumers have standard Dixit-Stiglitz preferences consuming the bundle
$$Y= \left(\sum_{i \in I} D_{i}^{\frac{1}{\varepsilon}} Y_{i}^{\frac{\varepsilon-1}{\...
5
votes
2answers
106 views
Elasticity of Substitution of CRS Production Function
Suppose that $F(\cdot)$ has CRS in $K$ and $L$, the elasticity of Substitution is $\sigma_{K L} \equiv F_{L} F_{K} / F F_{L K}$.
I once derived this equation but I remember that it takes me quite ...
3
votes
1answer
53 views
How to compute elasticity of substituion in general?
We know that the elasticity of substitution is defined as
$$
e=\frac{d \ln(x_2/x_1)}{d \ln(MRS_{12})}=\frac{\frac{d(x_2/x_1)}{x_2/x_1}}{\frac{d(MU_1/MU_2)}{MU_1/MU_2}}
$$
When we compute ES for CES ...
7
votes
1answer
86 views
When do workers versus capital owners share of income increase?
The share of total income obtained by workers rather than capital owners is for obvious reasons of interest. Assuming that the economy can be desribed by an aggregate production function
$$Y = F(K,L)$$...
4
votes
1answer
88 views
How to compute elasticity of substitution in labor market of blacks and whites using experience-education groups?
I'm reading "Competition in the Promised Land – Black Migrants in Northern Cities and Labor Markets", by Leah Boustan, and I'm trying to understand her computation of black and white ...
1
vote
1answer
29 views
Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes
I'm looking for an example of a family of production functions indexed by, say, rho, where the inputs become closer and closer to perfect substitutes as rho approaches 1, and yet, the marginal product ...
1
vote
1answer
83 views
Contradictory FOC and maximizing solution
I have to maximize the following function -
$\max_{x \in (0,1)} (((p_1x)^{2r} + (p_2(1-x))^{2r})/2)^{1/r}$
where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be ...
4
votes
0answers
28 views
In the BLP paper, why interacting consumer characteristic with product characteristic can generate more desirable substitution pattern
Got a question about the famous BLP paper (http://people.stern.nyu.edu/wgreene/Econometrics/BLP.pdf). When there is no interaction between product characteristic and consumer characteristic, the ...
2
votes
1answer
85 views
Meaning of «intertemporal substitution effect dominates the income effect»
Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, ...
3
votes
0answers
49 views
Why is my elasticity of substitution wrong?
I am calculating elasticity of substitution for the following production function:
$$F(K,L) = A(aK^{-\gamma}+bL^{-\gamma})^{-\mu/\gamma}$$
where $A, a, b, \mu, \gamma$ are constants. $A, a, b, > 0$,...
0
votes
1answer
31 views
Price elasticity of demand of CES
Anyone would like to help me show the following ( or a book/paper reference would be a great help)
" The price elasticity of demand is equal to $\sigma$ for the demand function of CES preference,...
3
votes
2answers
292 views
How was CES utility function derived?
Is there any book/papers that I can refer to the proof (derivation) of the CES utility function?
Or if anyone could help me with the derivation, I will be so much grateful to you.
3
votes
0answers
77 views
How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?
Statement: Let the dynamics of wealth of the agent satisfy
$$dX_{t} =
\pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$
where $(\pi,c)$ is an ...
1
vote
0answers
44 views
Capital in terms of labor
I have a question that asks to find $\frac{\partial K}{\partial L} $
from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
1
vote
2answers
58 views
Calculating price elasticity by asking a "this" or "that" question
Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example)
If I decrease the price of both goods by 10% and ask:
"Do you prefer A for 9 or B for 18 "
What sort of insights (...
2
votes
1answer
108 views
Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress
I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
2
votes
0answers
286 views
Negative elasticity of substitution in a CES production function
I have empirically estimated the elasticity of substitution parameter in the following model:
$$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho} $$
here, $Y_t$ is output, $A_i$ is a ...
0
votes
1answer
106 views
How to find the elasticity of substitution for the general CES-function?
I have to find the EOS for the general CES-function defined as
$$
y = (a_1x_1^p+a_2x_2^p)^{1/p}
$$
I first find $MP_1$ and $MP_2$ to find $MRTS$. We have that
$MP_1 = \frac{\partial y} {\partial ...
1
vote
0answers
113 views
Constant Elasticity of Substitution- profit maximization vs cost minimization
Consider the following production function:
$$
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
76 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
18 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
842 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
67 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
143 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
90 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
246 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
75 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
137 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
93 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
116 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
48 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
281 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
123 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:
$$\sigma = -\frac{d \ln (\frac{x_2}{x_1})}{d \ln(\frac{x_1}{1+x_2})}...
4
votes
1answer
470 views
Complementarity in CES Production Function
I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$),...
4
votes
2answers
171 views
Is optimal labour zero when (i) capital fixed and (ii) elasticity of substitution less than 1?
I am getting some "weird results". I find that in a CES, with short term fixed capital and elasticity of substitution smaller than one, it is optimal for firms to hire zero labour, which seems at odd ...
-2
votes
2answers
272 views
How do find elasticity of substitution for this function
The motive of my post is in search of some help in order to understand the correct way to find the elasticity of substitution by means of calculating the following function.
$$f(K, L)=\frac{K^{2}L^{...
1
vote
0answers
101 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{\...
4
votes
1answer
283 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
220 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
590 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 ...