# 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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### How can I obtain Leontief and Cobb-Douglas production function from CES function?

In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function, $$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$ (where the ...
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### Solow Model: Steady State v Balanced Growth Path

Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model: $$Y = K^\beta (AL)^{1-\beta}$$ I have been asked to derive the steady ...
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### Why is the Cobb-Douglas production function so popular?

As relatively novice quantitative analyst/ Cost analyst, Ive been asked to estimate the level of a given organizations productivity more than once, and then forecast for the next couple of periods. ...
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### CES: Production function: Elasticity of substitution $\sigma = 1/(1 + \rho)$

I have to prove that $\sigma = 1/(1 + \rho)$ for the CES production function: \begin{align} q = (l^\rho + k^\rho)^\frac{1}{\rho} \end{align} I found out that I need to solve the following equation: \...
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### CES Production Function with $\rho>1$

In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho}$, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the ...
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### Concave production function implies convex cost function

Let's assume we have an increasing production function $f:\mathbb{R^+} \to \mathbb{R^+}$ Now, assume this production function is concave and that the price of input z is fixed (this is a single-input ...
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### How to derive firm's cost function from production function?

I recently learned how to solve the following type of problem using the method of Lagrangian multipliers: Given a consumer with utility function $u(x,y)$, wealth $w$, prices $p =(p_x,p_y)$, budget ...
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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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### 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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### CES production function estimation

Introduction There are different ways of estimating the parameters of a production function. For example, single-equation and system equation techniques are both possible. Another difference among ...
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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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### 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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### 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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### Why labour, capital, and output levels cannot be pinned down in perfect competition?

Consider a firm producing with the following technology: $$Y = AL^{\alpha}K^{\beta}$$ Assuming that factors are paid their marginal contribution to output, it can be ...
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### Transformation Function

In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (...
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### Lessons From Successfully small island economies

What economic and development lessons/strategies can developing Caribbean countries learn from successfully small island nations like Singapore?
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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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### 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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### Mathematical derivation of the Production Possibility Frontier

What are the mathematical basics of production possibility frontier? How can I derivate it? Can I have an example for it?
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### CES v. Leontief Aggregator in Production

Consider a production process with two distinct capital types such that there is a capital aggregator. You could view $k_v$ as a more versatile capital (e.g. can be converted into many different ...
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### Is Artificial Intelligence a completely new (and underestimated) production factor?

Accenture research defines Artificial Intelligence as completely new production factor along labour and capital. Is such notion acceptable by economists? As far as I understand then every asset of AI ...
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### Examples of how economists come up with a production function for a firm?

I am a young man studying economics on his own. In every microeconomics text I find, they teach you what a production function is, but they never show examples (or practice problems) on how one comes ...
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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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### 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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