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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1answer
46 views

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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40 views

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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21 views

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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1answer
24 views

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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53 views

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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1answer
39 views

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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36 views

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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59 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 ...
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1answer
78 views

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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68 views

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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60 views

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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62 views

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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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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2answers
295 views

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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1answer
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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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40 views

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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Walras Law in a production economy with fixed costs

Consider a price taking firm with fixed costs $fc \geq 0$: \begin{align*} \Pi &= \max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\} \end{align*} A representative household owns this firm:...
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186 views

CobbDouglas: Constant marginal costs and constant returns to scale

A company has a production function: $$y=x_1^{\alpha}x_2^{1-\alpha}$$ where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its ...
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How do I work with the growth accounting framework in a regression?

I am currently writing my master's thesis with the topic "The impact of digitalization on economic growth in China and Germany". My idea is to take a technology such as Industry 4.0, IoT or ...
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1answer
70 views

How to find the cost function for perfect complements [closed]

Imagine I got a production function like it : $$ \min\{x_1, x_2\} $$ How can I find the cost function?
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1answer
63 views

Unbalanced panel data in prodest package in R

I have a question regarding the usage of unbalanced panel data for TFP estimation by using the prodest package. The dataset could be found here: https://drive.google.com/file/d/...
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1answer
85 views

Production function and elasticity

Let $y=x_1^\alpha x_2^\beta$ where $\beta=1-\alpha$ be a Cobb-Douglas production function. Find the elasticity of the optimal demand functions (for minimizing production cost) for both goods wrt. $w_2/...
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369 views

What is the returns to scale of the production function q = min {K, L^(1/2)}?

I learned that when there is decreasing returns to scale, the average cost is always increasing. But the professor told us today that the other way around might not always be true. So if average cost ...
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Inverting the production function - Okun's Law: Fit at 50? (BALL; LEIGH; LOUNGANI, 2012)

Consider the following equations: $$ \tag{1} E_t - E_t^* = \gamma \cdot (Y_t - Y_t^*) + \eta_t, \gamma > 0, $$ $$ \tag{2} U_t - U_t^* = \delta \cdot (E_t - E_t^*) + \mu_t, \delta < 0 $$ where $...
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1answer
146 views

Marginal cost given (Cobb-Douglas) production

My function is $y=x_1^\alpha x_2^\beta$ with $\beta={1-\alpha}$. I found: the minimization problem for demand to be $x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\frac{\alpha}{\beta} \right )^{\frac{\...
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How to explain the flattening of the SRAC curve?

I discovered that there is a way that Short-run average cost curve could become 'flatter' instead of shifting. Yet I cannot find an explanation of why and how it can become flatter. For example, in ...
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1answer
252 views

Finding the conditional input demand function

Find the conditional input demand function and cost function for the given production function $$f(a,b,c,d)=\min\{ a,2b\} + \max\{3c,4d\} $$ In The solution, The production function is defined as $f(x,...
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1answer
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A question about Nash Equilibrium

I have some trouble with Nash Equilibrium. The specific question as follows. Suppose that there are $2N$ people in the village, of which $N$ residents live in the first district, and each person ...
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1answer
148 views

If production function is concave, then demonstrate that profit function will also be concave

Show that concavity of firm's production function implies concavity of its profit function. (Hint: For a concave function, first order conditions gives the vector that maximizes the function) ...
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1answer
105 views

Elasticity Cobb-Douglas production function

I am given the production function $y=x_1^\alpha x_2^{1-\alpha}$, where $0< \alpha <1$ I found the demand functions for minimum production cost to be $ x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\...
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1answer
1k views

Calculate supply function based on production or cost function

Q1: A company has the following production function: $$f(x_1,x_2) = 2x_1 + x_2$$. The factor prices are $w_1=4$ and $w_2=3$. Calculate the company's supply function. Q2: A company's cost function is $$...
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2answers
281 views

Economic interpretation of Returns to Scale

There are three possible types of returns to scale: increasing returns to scale, constant returns to scale, and diminishing (or decreasing) returns to scale. If output increases by the same ...
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1answer
66 views

Estimating $TFP$ using Cobb-Douglas production function

Suppose we want to estimate total factor productivity (TFP) under time series framework. Let assume that the production function is given in the Cobb-Douglas form, i.e. $$Y_t=A_tK_t^\alpha L_t^\beta,$$...
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Prodest package in R for TFP estimation, gives different results

I have the following issue: each time I run the estimation of the TFP by using prodest package in R 4.0.3, I obtain different coefficients before the variables as well as omega variable is different: ...
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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. $A, a, b, > 0$,...
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3answers
204 views

Increasing returns, implications?

If a firm has increasing returns to scale (i.e., doubling inputs more than doubles output) would that firm logically end up being the sole firm in its sector in the long run? If not, what is the ...
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1answer
49 views

Does labor negatively affect output (from empirical perspective)?

I am estimating Cobb-Douglas production function for US using time series framework: $$Y_t=A_t \times L_t^\alpha K_t^\beta $$ where $Y$ is output, $A$ is $TFP$, $L$ is labor and $K$ is capital. After ...
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Arellano and Bond (1991) or Blundell and Bond (1998) in R estimation

I have the following problem with the Arellano and Bond (1991) or Blundell and Bond (1998) estimators in R using the plm package. I receive the following problem when trying to run the needed ...
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1answer
82 views

Empirically estimating TFP

Suppose we assume that production function has a Cobb-Douglass form: $$Y=A\times K^\alpha\times L^\beta,$$ where $Y$ is output (GDP), $A$ is Total Factor Productivity and $L$ is labor. By log-...
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2answers
83 views

Are prices part of total factor productivity?

I am trying to understand how production is related to income/profit and where do prices enter. Suppose there is a single firm with a Cobb-Douglas production technology: $$Y=AK^{\alpha}L^{\beta}$$ ...
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32 views

prodest package in R, TFP growth estimation

I have a question regarding the results and its transformations received from prodest package estimation. So, the dataset is available here https://drive.google.com/file/d/1aedWYABus1fQjKWxkOmYOmxv-...
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1answer
51 views

TFP in R via estprod package

I want to calculate the TFP by using the estprod function (I use R 4.0.2). As far as I understood the only way to calculate the TFP is manual following this logic . ...
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0answers
18 views

Which diagnostic tests are suitable for Measuring Total Factor Productivity (TFP)?

I did the TFP estimation with Levinsohn Petrin (in R) but I have doubts about the diagnostic tests e.g. I know that the estimation of autocorrelation in residuals has to be done (it would be very ...
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How was the Cobb Douglas function derived?

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the ...

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