Questions tagged [ces-function]
The ces-function tag has no usage guidance.
39
questions
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Are homothetic additively separable preferences always equivalent to CES?
Are homothetic additively separable preferences always a monotonic transformation of CES preferences?
In technical language, the question is the following:
Let $n>1$, and let $f:\mathbb{R}^n_{\ge 0}...
- 232
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2
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226
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What is an example of utility function where the proportion of one goes to zero?
I would like an example of an utility function with 2 goods where the proportion of one goes to zero (and the other goes to one).
I am thinking of a problem where the household receive an endowment y ...
3
votes
1
answer
113
views
CES production function: How to show that $\sigma < 1$ implies essentialness?
Consider the CES production function:
$$Y = f(K, L) = (a \cdot K^\rho + (1 - a) \cdot L^\rho )^{1/\rho}$$
The elasticity of substitution is $\sigma = 1/(1 - \rho)$. I remember that, if the elasticity ...
3
votes
1
answer
78
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Elasticity of substitution by regression: Biased results (simulation)
I have the following simulation problem:
Consumers, whose utility I know, go shopping for two goods. However, prices differ each time they visit a shop. Therefore, these consumers always purchase ...
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29
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Decomposition of preferences into set of CES functions
CES function as a tool
Hello everyone,
I have this idea: CES function basically tells us what is the elasticity of substitution between two (and more) goods, therefore giving us the exact complement/...
- 730
3
votes
1
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49
views
Explain the definition of a primal shifter versus an input shifter parameters in the standard CES function
I have run into a CES function that seems to be very closer to standard but with a small disaggregation of the share parameter into two parameters (primal share) and (input shift). I am hoping someone ...
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267
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Utility function distinguishing between complements/substitutes
Distinguish between complements/substitutes in utility function or production function
Hello everyone,
I would like to know if there exists some utility function $U(x)$ for $n$ goods that is able to ...
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178
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Confusing on the CRS Property of CES Function
Say a CES function is that $$Y = A\left[\alpha K^{\rho}+ \beta L^{\rho}\right]^{\frac{1}{\rho}}$$. Clearly this function is constant return to scale whatever the values of $\alpha$ and $\beta$ take.
...
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32
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on nested CES--derivation issue
I am reading Sachs and Kotlikoff (2012 NBER) and am wondering how they derive one equation in their paper. The setting is the following:
Their model is a variant of the standard two-period ...
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366
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A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes
So the most prominent preferences are perfect substitutes, perfect complements and cobb-douglas preferences. Perfect complements and perfect substitutes are extreme cases and I was asked whether there ...
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137
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Convex CES Aggregator
I just find it seems that a CES aggregator e.g. $\left[\sum_{j=1}^{J} N_{j}^{(\sigma-1) / \sigma}\right]^{\sigma /(\sigma-1)}$ with $\sigma<0$ is called a general convex aggregator and its limit as ...
- 2,297
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256
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Solving Cost Minimization with CES Production Function and Two Types of Input
A CES aggregator: $y=\left(\int_{0}^{1} y(i)^{\frac{\eta-1}{\eta}} d i\right)^{\frac{\eta}{\eta-1}}$, where $i \in[0,1]$.
For each intermediate good: $y(i)=\ell_{r}(i)+\ell_{c}(i) / a(i)$, where $a(i)$...
- 2,297
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94
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CES utility with negative values
We know that the CES utility function approximates a Leontief utility function as in the following:
$$u(x_1,x_2) = (x_1^{-r}+x_2^{-r})^{-1/r}\overset{r\rightarrow\infty}{\longrightarrow}\min\{x_1, x_2\...
- 41
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133
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Non CES Production Functions
I know CES production functions dominate economics, but I was curious, why? I've never seen a research paper or presentation utilize any form of a production function that is not CES.
My question is ...
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323
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The Intuition of CES Utility
Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$
1 The indirect ...
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301
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How to prove a generalised function is quasiconcave?
I have a question I have been asked to solve:
Given that $(a_1, a_2,...,a_n)\in R_{++}^n$ and $(x_1, x_2,...,x_n)\in R_{++}^n$, and $A>0, \mu >0, p \neq 0$, if there is a function $f(x)=A(a_1x_1^...
3
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0
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146
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What's special about Cobb–Douglas utility relative to the rest of the CES family?
My question concerns CES utility functions, which have the form
$$u(x) = \left(\sum_{j=1}^n a_j x_j^{\rho} \right)^{1/\rho}$$
for utility parameters $a_j$, an elasticity parameter $\rho$, and some ...
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536
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Log-linearization of CES production function
I am trying to recover the Log-linearisation of a CES production function in a paper. Although I am fairly confident with Log-linearisations, I simply do not find the supposed result.
The production ...
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136
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Nested/Recursive Dynastic Utility Functions
I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain ...
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168
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Bellman equation corresponding to stochastic EZW recursive utility
A bit of a basic question maybe, but I am confused how to write down the Bellman of this recursive utility function based on Epstein-Zin-Weil preferences and some stochastic constraints.
$$
U_t = \...
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101
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Is there a name for this type of CES look-alike utility function?
I do not know whether the following utility functions are used a lot but I was wondering whether there was a common name for this type CES like utility function
$$u(z) = \left[ \left( \sum_{j \in J_1}...
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114
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CES utility function in an Edgeworth box
Two consumers have the CES utility function $x_1^\beta +x_2^\beta$, for $0<\beta<1$, their initial endowments are $w^1=(1,0)$, $w^2=(0,1)$ Draw the Core of this economy in an Edgeworth box. Note ...
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86
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Homogeneous Utilities: Anything other than CES?
Does there exist any homogeneous utility function, i.e., $u(\lambda \mathbf{x}) = \lambda u(\mathbf{x})$, that is not a special case of the CES (or nested CES) family of utility functions or its ...
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59
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Parameter value for a CES production function
Consider a firm with the following CES production function, which utilizes only two production factors (capital and labor) whose prices are, respectively, $r > 0$ and $w > 0$:
$$ y = \gamma \...
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692
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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 ...
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146
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CES aggregator for intermediates with heterogeneous productivity
I'm following Atkeson, Burstein (2019 JPE), and cannot understand the aggregation result.
There is measure $M(z)$ of firms with productivity $z$, with production function
$$
y(z) = z k(z)^\alpha l(z)^...
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52
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Can you set $C / P^{\eta}$ to be the numeraire in a NK model?
Consider a static model with CES demand. Real aggregate demand is
$$
C = \left(\sum_j c_j^{(\eta-1)/\eta}\right)^{\eta/(\eta-1)}
$$
and labor supply is inelastic, so the budget constraint is
$
\sum_j ...
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Estimating CES utility (not production) function parameters
The CES utility function has the form
\begin{equation}
u(x_1,\dots,x_n)=\left[\sum_{i=1}^n\alpha_ix_i^\rho\right]^{1/\rho},
\end{equation}
where $\alpha_i$ is the consumption share parameter and $\...
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Derivation of demand function
Hello.
I'm graduate student in Japan.
This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function.
This ...
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CES production function profit and supply function
I need to derive the profit function for the following CES function: $$ f(z) = (\sqrt{z_{1}^{\rho} + z_{2}^{\rho}})^{1/ \rho}$$ where $\rho \leq 1$. This is the answer that I am supposed to be getting:...
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On complements and substitutes with a CES function
Define the CES function $q : \mathbb R_+^n \to [0,1]$ by
\begin{align}
q(x) = \left[\frac{1}{n}\sum_{j=1}^n{x_j^\frac{\sigma-1}{\sigma}}\right]^\frac{\sigma}{\sigma-1}
\end{align}
where $x \in \mathbb ...
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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 ...
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877
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Nested CES Production Function
If I have four input factors (a, b, c, b) and I want to construct a nested CES production function such that (a, b) are substitutes, (c, d) are substitutes and [(a, b), (c, d)] are complements, I.e. a,...
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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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CES function estimation
For a paper I was using the micEconCES package to estimate the CES production function for a country at the aggregate. For a two-input function with capital and labour I used for the variables the ...
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Choosing Data for CES Production Function
So I am currently trying to write a paper estimating the Constant Elasticity of Substitution Production Function of the USA. I am using the simple version with two inputs capital and labour. Since the ...
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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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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-...
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