# 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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• 1,048
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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. $A, a, b, > 0$,...
• 1,833
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### Can technical change have a negative growth rate?

Using the following nested CES function I have backed out augmentation indices $A_L$ and $A_E$. Where $A_L$ is a labour-augmenting technical change index and $A_E$ is an energy-augmenting technical ...
4k views

### 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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• 121
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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 ...
• 497
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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 ...
• 109
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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 ...
• 1,990
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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 ...
300 views

### When is the PPF convex to the origin?

Given a 2X2 model (2 goods, 2 inputs), if the factor intensities (capital/labour ratio) of the two goods along the Pareto set are unequal, then we get a concave PPF. Can we get a convex PPF in some ...
• 227
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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-...
• 21
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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 ...
• 151
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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. ...
• 8,355
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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 ...
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### Fisher Separation with negative interest rate

In class we discussed Fisher Separation which states that the investment decision is independent of the financing decision. The optimality conditions are that MRS = MRT = (1+i) (i = interest rate). ...
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1 vote
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### Derivation from Solow-type neoclassical growth equation?

In Chapter 6 of the 12th edition of "Economic Development" by Michael P. Todaro & Stephen C. Smith, an equation is introduced to illustrate the consequences of rapid population growth, ...
1 vote
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### Introducing productive sector into an exchange economy where only one agent is endowed with input

I'm trying to find a competitive equilibrium for an economy with consumers and some outside productive sector. Consider an economy with two consumption goods $x_1, x_2$ and two individuals $A,B$ . ...
1 vote
25 views

### Toy model equilibrium calculation: How a small system's firm determines wage and price?

I am trying to model a small system, with limited population and a single firm. Personally I have no economic background but only taken a simple microeconomics course and I am quite interested in ...
1 vote
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### From Cobb-Douglas Production Function to Profit Function

A firm's output is given by the Cobb-Douglas production function $$Y_t=X_tK_t^{\alpha_K} L_t^{\alpha_L}$$ where $\alpha_K\approx\frac{1}{3}$ is the capital share and $\alpha_L$ the labor share. ...
• 323
1 vote
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### Why is the Hicksian form of the CES demand used in CGE model forms rather than the Marshallian

I am curious to know why the Hicksian form of the CES is used in CGE models rather than the Marshallian form. I have a few hypotheses, but I am not sure which one is correct. If any? Hypothesis 1: In ...
• 11
1 vote
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### Stata command for Dynamic Panel Production Function estimation

Consider a production function to be estimated, $$(*) y_{it} = \beta_0 +\beta_k k_{it} +\beta_l l_{it} + a_i +\omega_{it} +\varepsilon_{it}$$ where $\omega_{it}=\rho\omega_{i,t-1}+\xi_{it}$. The ...
• 3,643
1 vote
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### Technology Parameter In Converted Minimisation Problem

Question: I want to understand what's going on with respect to the technology parameter $A$ when i convert this minimisation problem into a maximisation problem. The issue is only revealed when i use ...
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1 vote
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### Conceptualising the effect of changes to the substitution parameter in a CES production function

I'm trying to have a conceptual understanding of what happens to the CES production function when the substitution parameter $\rho = \frac{\epsilon - 1}{\epsilon}$ changes, where $\epsilon$ is the ...
• 11
1 vote
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### Total factor productivity (TFP) estimation in R via estprod package

good morning I am trying to calculate the total factor productivity (TFP) for companies in the manufacturing industry through the Levinsohn-Petrin model. To do so, I use the prodest package in R. ...
1 vote
123 views

### Find cost function for given production function

I have the following production function $$f(x_1,x_2,x_3,x_4)=max\{\min\{x_1, x_2), x_3+2x_4\}\}\ge q$$ And I want to find the cost function. What I think (1) $P_1+P_2 <P_3$ and $P_3/P_4<1/2$ ...
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1 vote
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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. ...
1 vote
225 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 $r$ ...
1 vote
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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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1 vote
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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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### Capital in terms of labor

I have a question that asks to find $\frac{\partial K}{\partial L}$ from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
1 vote
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### If the relative share of inputs is constant in a production process, does that mean that the inputs are used in fixed proportion?

One of the assumptions in Euler's adding up theorem is: Fourth, the relative shares of the factors are constant and independent of the level of the product. Does this mean that the factors are ...
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