Linked Questions

1
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1answer
569 views

How does the limit of $U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}}$ as c approaches 0 yield the Cobb-Douglas utlity function? [duplicate]

\begin{equation*} U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} \end{equation*} I ask this mainly because after logging both sides of the Utility equation (the first step to proving the assertion, I ...
0
votes
0answers
25 views

Can someone help me prove that the CES function is also a Cobb-Douglass function [duplicate]

I would like some assistance with a problem that I have showing a CES function is also a Cobb-Douglass utility function. Question: we have a CES function: $Y=A[\alpha K^{((1-\sigma)/\sigma))}+(1-\...
1
vote
4answers
2k views

Weird Leontief production function

I am solving some micro related exercises and I came across this weird Leontief production function: $$Q =\left(\min\{K, L\} \right)^b$$ I am not sure how to solve it. I have to find the inputs' ...
10
votes
3answers
2k views

CES Production Function with $\rho>1$

In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho} $, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the ...
7
votes
2answers
1k views

Constant Elasticity of Substitution: Special Cases

Take an $n$-commodity constant elasticity of substitution utility function, $$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$ How do we show the following: Show that as $\rho \...
4
votes
1answer
762 views

In the C.E.S. utility function do the parameters need to add up to unity to obtain the Cobb-Douglas utility function?

Consider the C.E.S. utility function $$U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} $$ Is it true that we must have $a+b=1$ in order to obtain a Cobb-Douglas utility function as $c\rightarrow 0$?
3
votes
1answer
774 views

Cobb-Douglas nested in CES model

Assume, using the following equation $Y=[((A_1L)^\alpha K^\beta)^\sigma+ (A_2X^\gamma)^\sigma]^{1/\sigma}$, we back out (obtain) the evolution of $A_1$ & $A_2$. Can we interpret $A_1$ as labour-...
-1
votes
1answer
1k views

the difference between cobb-Douglass and leontief production technology [closed]

whatis the differences between cobb-Douglass and leontief production technology
0
votes
2answers
224 views

How can I prove $U(x) = [𝛼_1𝑥_1^𝜌+𝛼_2𝑥_2^𝜌]^{(1/𝜌)}$ is equal to Cobb-douglas Utility function when $𝜌\rightarrow0$ [closed]

This is the question, I have problem with part b, I don't know what function should I use to reach the result thanks in forward
3
votes
1answer
167 views

Interpretation of Interesting Utility Function

Solving introductory microeconomics problems I have come across the following type of utility function: $$ f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{...
2
votes
1answer
292 views

What is the economic meaning of distribution parameter in a CES-production function?

This is the production function (two input factors: $x_1$ and $x_2$) $$q=A[δx_1^ρ+(1-δ)x_2^ρ]^{\frac{1}{ρ}} $$ If distribution factor $δ$ is set to increase, what are the economic impacts on these ...
2
votes
1answer
200 views

CES v. Leontief Aggregator in Production

Consider a production process with two distinct capital types such that there is a capital aggregator. You could view $k_v$ as a more versatile capital (e.g. can be converted into many different ...
2
votes
1answer
61 views

CES production function with non constant returns to scale

In the equation \begin{equation} Y=\left[ aK^{\frac{\sigma -1}{\sigma }}+\left( 1-a\right) L^{\frac{\sigma -1% }{\sigma }}\right] ^{\frac{\mu \sigma }{\sigma -1}} \label{ces_pf} \end{equation} if $\...