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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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### 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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### 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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### 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. ...
11k views

### 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: \...
34k views

### 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 ...
2k views

### How does inflation impact the welfare of the economy?

When the government causes inflation through printing money, the individuals who saved their money in the bank are poorer. Is there a way to determine how different inflation rates impact the welfare ...
6k views

### 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 ...
854 views

### 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 ...
985 views

### 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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### Is a production function bilinear?

I believe the following is the multiplicative property of bilinearity: $$Y=F(K,AL)$$ $$c_1 F(K,AL) = F(c_1 K, AL)$$ $$c_2 F(K,AL) = F(K, c_2 AL)$$ But when we have multiplied through the ...
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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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### 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 ...
514 views

### Estimating elasticity of substitution in nested CES functions

I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following ...
758 views

### Why labour, capital, and output levels cannot be pinned down in perfect competition?

Consider a firm producing with the following technology: \begin{equation} Y = AL^{\alpha}K^{\beta} \end{equation} Assuming that factors are paid their marginal contribution to output, it can be ...
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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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### Could someone please explain the proof of Hotelling's lemma?

According to https://en.wikipedia.org/wiki/Hotelling%27s_lemma, the maximum of the firm's profit at some output is given by the minimum of the difference between the profit and the revenue. However,...
312 views

### Complementarity in CES Production Function

I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$),...
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### Can capital still be paid its marginal product in the absence of a homogeneous capital stock?

Thomas Piketty's best-selling book on inequality, "Capital in the Twenty-First Century" has attracted a lot of criticism on the right for its data analysis. Less well-known, however, is the criticism ...