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Questions tagged [production-function]

A function whose value is the produced quantity associated with a given vector of factor inputs. The production function represents the technology available to the firm.

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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 ...
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What's the relationship between Output elasticity and Returns to scale?

https://en.wikipedia.org/wiki/Output_elasticity "If the production function contains only one input, then the output elasticity is also an indicator of the degree of returns to scale. If the ...
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How to derive optimal labour supply from utility? [on hold]

I am struggling with this question: An agent's utility is U = log(C) - 2L2 (where log(C) is the natural logarithm). The agent produces their own output with a production function C = Y = AL^α, where ...
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Economic interpretation of a CES production function

I am following a paper where a production function of this type is used. $$Y=\left [\beta K^{- \rho}+\alpha \eta \left (\frac{K}{L} \right )^{-c(1+\rho)}L^{- \rho} \right ]^{-1/\rho}$$ It is a ...
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Derive the cost function for a Homothetic production function

I'm having trouble understanding the steps in showing that a Homothetic production function's cost function must be expressible in the form $C(w, q) = a(w)b(q)$. Since the production function is ...
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Deriving the translog production function

Ive been having difficulty deriving the translog production function defined as: $$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$ I know ...
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General Equilibrium Involving Production

I need a little conceptual clarification. For a standard $N*K*M$ general equilibrium model, would an allocation, say, $y^k$ be Pareto Optimal if it does not solve $max(py^k)$? I understand that the ...
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Is the CES a special case of the translog production function?

I was discussing today with a classmate about the relationship between prodution functions, and we tried to prove that the CES is a special case of the translog production function, but we failed. We ...
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Diminishing MRTS range

So I was solving a question which says find the range in which MRTS is diminishing $f(k,l) = 600k^2l^2-k^3l^3$ is the production function I got the MRTS = $ -(1200kl^2-3k^2l^3) \over 1200k^2l-3k^3l^2$ ...
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Marginal Product and Average product

So I've seen in my textbooks and many places online that when marginal product is more than average product average product is increasing, when average product is falling average product is greater ...
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Whats the rationale for using taylor series in economics?

I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series. Why not just leave the function as ...
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Homogenous production function

Could one define a production function which is homogenous as having constant elasticity of substitution. Just want clarification . Thanks
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Why does a homothetic function have constant ratio of marginal products along rays?

A homothetic ordering is defined as $x \succeq y \Rightarrow \lambda x \succeq \lambda y \qquad \forall \lambda >0$ where $x,y \in \mathbb{R}^n$ Then, any differentiable function representing ...
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Derive the cost function and supply function from production function

I didn't study economics, but am quite interested in the topic. I came to the question whether I could derive the supply curve / marginal cost function from the production function and I actually ...
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Is “$ f(k,l) \: is \: decreasing\:return\:to\:scale \Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$” always true?

For the productions $f(k,l) $ that are continuously differentiable, is the proposition that "$ f(k,l) \: is \: decreasing\:return\:to\:scale \Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$" always true, ...
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How to prove if production set Y satisfies free-disposal and CR of scale, then Y is convex, when there are only 2 commodities

Free-disposal and CR of scale can not imply convex production set. But it is true for single-input and single-output model. Therefore, I am wondering how to prove if production set Y satisfies free-...
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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} & ...
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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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Decision over “max” production function:

I've been presented with the following problem: $$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$ And the objective is to both maximize profit and minimize cost. First of all, if the problems are ...
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Euler's Theorem

Can anyone give me connection and intuition behind each of the following euler's equation- Euler's equation in production function represents that total factor payment equals degree of homogeneity ...
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Quasiconcavity and homogeneity

How to prove that if $f$ is strictly quasi-concave and homogeneous of degree 1, then $f$ is concave? It was left as an exercise by Silberberg & Suen (2001), p.140. I simply could not elaborate ...
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2 firms production decision for one agent

I'm trying to solve the optimal production $\{x,y\}$ for a risk neutral agent with weight $w$ in firm $X$ and weight $1-w$ in firm $Y$. Each firm has marginal cost $c^X$ and $c^Y$ respectively. The ...
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General Equilibrium with Linear Production

I don't think I understand how optimization problems with a linear function work as of now. If you have a production economy with two agents, two goods and Cobb-Douglas utility representation, and you ...
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Price Derivation in a Production Function

Here is a composite goods production function: And here is the price ratio of Ys and Yg, derived from their marginal products: Then the author normalized the price of final goods Y to 1 and somehow ...
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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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Cobb Douglas Production Function Substitutes or Complements?

I see that there is a question similar to mine but it is does not specifically answered. Here is my question: I understand that, in a Production Function, when elasticity of substitution is greater ...
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intuitive interpretation of the marginal return/productivity of capital being less than one

Let's assume you have a production function, f, and you want to know how the output changes with respect to capital, everything else constant (ceteris paribus), so you want to know the marginal ...
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Interpretation of the Cross Partials of the Cobb-Douglas

Consider a Cobb-Douglas Prod. Function $$Y=AL^{a}K^{1-\alpha}$$ This has the cross-partial: $$\frac{\partial^2 Y}{\partial K\partial L}=(1-\alpha)\alpha AL^{\alpha-1}K^{-\alpha}$$ Is the ...
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Is there an economic interpretation of the production transformation function?

The production set has a simple meaning: It is the set of all production vectors that are feasible to a firm. The production function also has a simple meaning: It gives the output quantity for a ...
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Question on returns of scale in isoquants

What does the dotted line in the diagram show and what are they called? I am also wondering why the steepness of the isoquants changes at Q=3 for the third diagram. Thanks
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Production function question

Some help with this would be appreciated.
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Perfect complement graph and isoquant

$f(x_1,x_2) = min \{x_1,x_2\} + x_2$ if that was the production, what would the isoquant be? Would it simply follow $x_1 = x_2$? I'm not entirely sure what it the graph would look like.
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Partial production function question

Hi everyone, I am learning about the partial production function. I don't understand why a tangent it drawn next to the curve; I get that it shows the MPL. Does this mean diminishing marginal product ...
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Estimating production functions with time series data

A while back I asked How do we estimate production functions? The answers given address cases when dealing with cross-sectional data, However most of the data I've been seeing is given by a time ...
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Impact of Natural Disaster on Production Function

Say a natural disaster strikes. People were killed but the losses were small relative to the size of the work force. However, many buildings and infrastructures have been severely damaged. I'm ...
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Is it constant returns to scale if the output of a production function is purely a function of one variable?

For $Y=F(K,L)= 2L$ If I multiply them by an constant $z$: $Y= F(zK,zL0)$, i'll get $2(zL) = z(2L)$. Inputs increase proportionally therefore constant returns to scale. This doesnt seem right ...
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How does hedging using futures work?

I can't understand how it makes sense. From what I've read, corn producers (for example) sell their corn at current price but deliver the corn later, in order to protect themselves from decline in ...
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Estimating Endogenous vs Exogenous growth models

Exogenous economic growth models (mostly those that take technological progress, or change in TFP as exogenous and random) are rather easy to estimate econometrically. But how about endogenous ...
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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 ...
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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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How change in technology affects the price of labour and capital?

If the technology improves how does the price of labour and capital change. We take the neo-classical assumption that demand for each factor depends on it's marginal productivity, and demand and ...
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Understanding the Zellener-Revankar Production Function

I took out a book from my university library called Econometric Modelling with Time Series: Specification Estimation and Testing in an attempt to understand the importance of MLE in Econometrics. ...
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How was the CES production function derived?

The Constant Elasticity of Substitution production function is defined as: (Taken from Wikipedia) $$Q=F \boldsymbol{\cdot}\left(a\boldsymbol{\cdot}K^r+(1-a)\boldsymbol{\cdot}L^r \right)^{1\over{r}}$$...
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Aggregate production function, factor shares and cointegration

When estimating an aggregate production function you fit your data to a selected functional form of the production function, derive the parameters and inference from there. My question is, is there ...
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Anything written on the process behind “multiplicative” production function?

Intuitively, one might make a naive first guess that the production function of the economy, or of a firm, should be a "leontief" production function: "for example, you need both a factory and a ...
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How to determine sensible values for economies of scale?

I'm analysing a contest-game in which players exert effort to increase their chance of winning. Each player has a has a cost of marginally increasing their probability of winning the contest given by $...
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list of exotic production functions?

Standard production functions are Cobb-Douglas, CES, Leontief. The most exotic production function I have seen is the Ethier production function. I am wondering whether there is a book/list of ...
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Consider the following production function $Q=min \left(\frac{L}{2a}, \frac{K}{4b}\right)$. Let $w$ and $r$ be the wage and rental rate respectively [closed]

The cost function associated with this production function is $A) 2awQ\\ B) 4brQ\\ C) (wa + 2br)Q\\ D) None\; of\; the\; above$ What I have tried is: We have the cost function $wL+rK=C$. Since, here, ...
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modelling Inconsistent production functions

last year I asked How do we estimate production functions?. That answer provided was insightful from an econometric perspective and has helped me in applying such an understanding to the workplace. ...
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How to find the “cost function” given the production function *as well as* the cost per unit produced and the fixed costs?

I'm working on the following homework problem, transcribed verbatim: A firm has a production function defined as $y = 8L^{1/4}K^{3/4}$. The firm faces costs of \$20 wage, \$60 rental rate of ...