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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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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stone geary production and Multiple equilibria in a simple solow model: Do complex roots mean anything?

I have been looking at a simple solow model with stone geary production technology and law of motion of capital specified as follows: $$f(k_t)=(k_t-\bar{k})^{0.5}$$ $$k_{t+1}=(1-\delta)k_t+sf(k_t)$$ $$...
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When does a CES production function have a weakly convex isoquant

Some CES production functions have weakly (but not strongly) convex isoquants; e.g., perfect substitutes. Under what general conditions do CES functions have weakly convex isoquants?
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Prove that if a production function is such that f'>0 and f''<0, then f'<Average Product

I was told in class that if we have a production function such that $f'(x)>0$ and $f''(x)<0$, then we have that the marginal product is less than the average product. That is $f'(x)<\frac{f(x)...
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How to calculate Returns to Scale for Translog production function with two inputs?

I have a double-log (both inputs and output in logarithmic form) translog production function with 2 inputs [with Labour and Capital]. There are two squared terms, one for each of the inputs and there ...
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What's the difference between fixed and variable O&M costs in power generation

Not sure what the difference is btwn Fixed and variable O&M costs. As you can see in this screenshot, both contain maintenance cost. While fixed o&m contains regular and irregular maintenance ...
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isoquant of a leontief production function

Consider a firm that can produce q units of good G using two technologies and two production factors, $z_1$ and $z_2$. There are two ways how a firm can produce the good G: It can use 2 units of $z_1$ ...
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Deriving factor allocation of production function

I am trying to solve an allocation problem for a nested CES production function with three factors. The production function we posit is: $$ F(K, \mathbf L, \mathbf C) = [\alpha K^\rho + \sum_{i\not\in ...
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Cobb Douglas Production: Identification issues for technical change

It's well know that under a Cobb Douglas production function, capital and labor augmenting technical progress cannot be individually identified. Accordingly, people usually assume Hicks or Harrod ...
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How do you convert or move from a linear cost function to a quadratic cost function?

I am reading a book on electricity cost modelling. I understand equation 2.7 below, which indicates that the total cost for an ith plant is a function of fixed cost(FC), fuel cost(FL), plant ...
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Intuition behind value added as TFP measure

In some papers the authors use value-added over capital and labor as TFP measure, what is the intuition behind this? For example, in one paper I just read the authors use $ \frac{VA}{(p_{K}K + p_{L}L)}...
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Cobb-Douglas Production Function - Finding units of labour to maximise production

Given production function $f(L,K)=16L^\frac{1}{4}K^\frac{3}{4}$, where each unit of labour costs £50 and each unit of capital costs £100 and you have a budget of £500,000. Find the number of units of ...
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In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?

The following is what I understand, so far. If we measure labour in the $x$-axis and capital in the $y$-axis, the slope of diagonal of the box is the capital-labour ratio $K/L$ in the economy. Let $A$ ...
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What are the advantages of Cobb-Douglas over a translog function?

I am carrying out an empirical study wherein I have to judge productivity for two inter-country alliances. While the translog is a better method theoretically the coefficients are insignificant, ...
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Why are production functions linear in technology?

Economists often assume a production function of the form $ Y = A f(K, L) $, where $Y$ is output, $K$ is capital, $L$ is labour and $A$ is technology. This form of production function can describe ...
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Finding production given total cost (shephard's lemma)

Given a total cost function, for example, $$ C = q {w}^{3/4}{v}^{1/4} $$ and Shephard's Lemma, how do you find the underlying production function $q(k,l)$? For this example, Shephard's Lemma provides ...
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What kind of production function would give a cubic-shape cost function?

I would like a production function that gives a cost function with the following shape: The figure was taken from "Microeconomic Theory: Basic Principles and Extensions, 12th edition", on ...
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Harrington Emerson and his 12 principles of labor productivity

Are these principles currently relevant? Which principles would you add or, on the contrary, exclude? Which principles are observed today, and which are not? Why? Which of the principles would you ...
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Estimating a stochastic production function with MLE

I am new to MLE programming and have never done it on Stata before. I am estimating a stochastic production function following Just-Pope (1978). The formula is the following: I understand in theory ...
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What is the elasticity of Substitution of the function X = (K+alpha)(L+beta)

For this function, the marginal rate of technical substitution is given by (K+alpha)/(L+beta). Generally we solve for K/L in terms of MRTS of two factors. Then differentiate to solve for elasticity of ...
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Normalization of production function

Can we normalize a production function in the same way we can normalize a utility function? For example, consider the CES function $$ F(x; A, a, \rho, \nu) = A \left( \sum_{i=1}^n a_i \, x_i^\rho \...
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If I have a production function f where the marginal product of all the input is constant, can f exhibit decreasing returns to scale? [duplicate]

Marginal product of input xi= \begin{equation} \frac{\partial f }{\partial x _{i}} \end{equation} Decreasing return to scale: f(tx,ty) < t f(x,y) for t>1
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Complementary input production function

I was looking for some complementary functions to work with. Let me state my problem first. I have two different households and I want to distribute them some money based on their characteristics. I ...
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Question on a passage from N.OKISHIO's Constant and Variable Capital

Sorry if this a dumb question, I am an undergrad economics student and am currently reading this paper from Okishio on the Marxist concept of Constant and Variable capital, my issue is on this ...
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CES production function parameter estimation

I'll ask a simple question. Since I have to find the marginal productivity of capital for all 19 euro area countries, I have to estimate some production functions. I started with the most obvious, i.e....
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Does global maximum of CRS Cobb-Douglas profit exist

In most macroeconomic papers it is taken as given that the aggregate prodution function is $Y=AK^{\alpha}L^{1-\alpha}$, and that the optimality conditions for inputs determine input demands: $$ \max_{...
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Error while estimating a production function with prodest package in R

I have an unbalanced panel with 15063 firms between 2012 and 2018. I am using this code to estimate the production function with Levinsohn & Petrin method: ...
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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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Doraszelski and Jaumandreu (2018) Intuition

Doraszelski and Jaumandreu (2018) estimate a CES production function with two forms of productivity shocks (1) labor augmenting and (2) Hicks neutral. They claim that the increase in labor augmenting ...
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Example of production function with negative returns with respect one input

Are there examples of production functions where increasing the input of one factor and keeping the other factor constant leads to reductions in total production?
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Idea Production Function References

I've read in growth theory about the Idea production function: $\dot{A}=f(A,S)$ which states that the change in ideas or blueprints or patents is a function of past ideas and the number of scientists. ...
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How is the translog cost function derived?

I realize that the translog production function is derived as a second order taylor approximation of a production function (e.g. the CES-production function), as explained in this post. Is the ...
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Linearization and the effect of a change

There is the following system of four equations and four endogenous variables $(K,L,w,q)$. Assume $F$ is a concave function. $\partial F(K,L)/\partial K = r + (1-p)$ $\partial F(K,L)/\partial L = w$ $...
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What does "the event of economic consequences" mean?

I read a paper talking about the Operating Cycle. On page 6th, they said: Sales of assets, no matter how disguised, are one-time events. In contrast, cycling capital through the cycle and generating ...
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Self-dual production functions that do not satisfy weak homothetic separability

I am looking for parametric production functions that do not satisfy weak homothetic separability (as first defined in Shephard, 1953), but that do allow for an analytical expression of the dual cost ...
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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 ...
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Production Set: Not satisfying Free Disposal Assumption

I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads ...
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Why does LRAC not connect the minima of SRAC curves? [duplicate]

Can anyone please provide an intuitive explanation and proper mathematical reason for non-intersection of SRAC and LRAC at the minimas of SRAC? I am seeing conflicting [1] [2] answers on the site ...
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Finding long run total cost function

I am trying to find the long run total cost function, given the firm's production function $y=L^α K^β$ where $α,β>0$ and two inputs $L$ and $K$ where $ L,K∈R_+^2$, with factor prices $w$ and $r$ ...
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Replicate Blundell and Bond (2000) results using R

I want to replicate Blundell and Bond (2000) Table III in R. I'm using the function pgmm from package plm, which (apparently) ...
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Relation between marginal cost and output elasticities

Does anyone know of any results that show the link between marginal cost and the output elasticities analytically? I am looking at production and cost theory books but can't find any results that ...
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I need to prove how an increase in output p increases profit-max. Can someone help to understand why IFT implies that z is a unique maximizing point? [closed]

MWG 5C6 asks: "Suppose a concave prod function f(z) with inputs $(z_1,...,z_L-1)$ and also that $\partial f(z))/\partial z_l \geqslant 0$ for all l and $z\geqslant0$ and that $D^2f(z)$ is ...
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7 votes
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How to get this Production Function in Growth Rates

I'm struggling to understand how Khan & Reinhart (1990) go from the next production function. $$y=A f(K,L,Z)$$ Where $y$ is the production of the economy, $A$ is a variable which contains the ...
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Under what condition is a cost function strictly concave in prices?

Define the unit cost function as $$ c(w) = \min_{z\geq 0} w\cdot z $$ subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
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Social Planner problem: two period

The production function is $F(K_t,N_t)=AK_t^\alpha N_t^{1-\alpha}$ and depreciation $(\delta)$ is equal to 1. The given preferences are as follows: $$U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(...
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References on Cobb-Douglas Function

I am wondering why everybody uses Cobb-Douglas production functions? Nowadays they are so standard that they are just written down without further discussion. Does anybody know more about this and can ...
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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 ...
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Quasi-Linear Production and Inefficiency

For quasi-linear production of $F(K,L)= \sqrt{K}+L $. I know for the optimal efficiency to exist $q \geq \frac{w}{2r}$ where w is the cost labour and r is the cost of capital. My question is what ...
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How does aggregate production function shift by an increase in average and marginal productivity of labour?

Increasing productivity would mean increase in output for each given amount of labour employed, resulting in an upward shift of production function as shown below. However I'm unable to understand the ...
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How can I add a multidimensional panel to estimate TFP (year, id, region) in R?

I'm not sure about adding fixed effects for the variables year,id,region (using the estprod library) as in this paper using LP stimator. In the STATA forum ( #18 #...
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