Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

1
vote
0answers
26 views
2
votes
0answers
44 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 ...
0
votes
0answers
185 views

Question about an economy with 3 components household, firm and government with functions given

I've spent considerable amount of time on this question, in vain. It is from one of the competitive exams for admission to a grad econ program. Help would be tremendously appreciated. Thanks. An ...
0
votes
1answer
59 views

Solve for the steady state with CRS Cobb-Douglas, problem with the system of equations

There is one agent with utility function given by: \begin{equation} U(c,l) = \frac{c^{1-\sigma}}{1-\sigma}-\frac{l^{1+\gamma}}{1+\gamma}\tag{1} \end{equation} With budget constraint: \begin{...
3
votes
2answers
104 views

Cobb-Douglas production function, given $w$ get $r$ regardless of input levels. Why?

There is a market economy with technology given by: $$Y = K^\alpha L^{1-\alpha} \tag{1}$$ Firms behave competitively and input prices are: $$r = \alpha K^{\alpha-1}L^{1-\alpha} = \alpha(\frac{L}{K})...
0
votes
1answer
74 views

In a perfectly competitive industry, why is apple considered best example of commodity? [closed]

Out of these options, shampoo apples ice cream hotels Why is apple considered to be the best example of commodity in a perfectly competitive industry? And Why not others?
2
votes
1answer
52 views

What is the economic meaning of distribution parameter in a CES-production function?

This is the production function (two input factors: $x_1$ and $x_2$) $$q=A[δx_1^ρ+(1-δ)x_2^ρ]^{\frac{1}{ρ}} $$ If distribution factor $δ$ is set to increase, what are the economic impacts on these ...
2
votes
1answer
115 views

What's the relationship between Output elasticity and Returns to scale?

https://en.wikipedia.org/wiki/Output_elasticity "If the production function contains only one input, then the output elasticity is also an indicator of the degree of returns to scale. If the ...
0
votes
0answers
36 views

Economic interpretation of a CES production function

I am following a paper where a production function of this type is used. $$Y=\left [\beta K^{- \rho}+\alpha \eta \left (\frac{K}{L} \right )^{-c(1+\rho)}L^{- \rho} \right ]^{-1/\rho}$$ It is a ...
1
vote
2answers
76 views

Derive the cost function for a Homothetic production function

I'm having trouble understanding the steps in showing that a Homothetic production function's cost function must be expressible in the form $C(w, q) = a(w)b(q)$. Since the production function is ...
3
votes
2answers
143 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 ...
0
votes
1answer
55 views

General Equilibrium Involving Production

I need a little conceptual clarification. For a standard $N*K*M$ general equilibrium model, would an allocation, say, $y^k$ be Pareto Optimal if it does not solve $max(py^k)$? I understand that the ...
3
votes
1answer
108 views

Is the CES a special case of the translog production function?

I was discussing today with a classmate about the relationship between prodution functions, and we tried to prove that the CES is a special case of the translog production function, but we failed. We ...
1
vote
1answer
39 views

Diminishing MRTS range

So I was solving a question which says find the range in which MRTS is diminishing $f(k,l) = 600k^2l^2-k^3l^3$ is the production function I got the MRTS = $ -(1200kl^2-3k^2l^3) \over 1200k^2l-3k^3l^2$ ...
1
vote
1answer
78 views

Marginal Product and Average product

So I've seen in my textbooks and many places online that when marginal product is more than average product average product is increasing, when average product is falling average product is greater ...
1
vote
1answer
62 views

Whats the rationale for using taylor series in economics?

I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series. Why not just leave the function as ...
1
vote
1answer
39 views

Homogenous production function

Could one define a production function which is homogenous as having constant elasticity of substitution. Just want clarification . Thanks
2
votes
1answer
78 views

Why does a homothetic function have constant ratio of marginal products along rays?

A homothetic ordering is defined as $x \succeq y \Rightarrow \lambda x \succeq \lambda y \qquad \forall \lambda >0$ where $x,y \in \mathbb{R}^n$ Then, any differentiable function representing ...
2
votes
0answers
489 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 ...
0
votes
1answer
34 views

Is “$ f(k,l) \: is \: decreasing\:return\:to\:scale \Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$” always true?

For the productions $f(k,l) $ that are continuously differentiable, is the proposition that "$ f(k,l) \: is \: decreasing\:return\:to\:scale \Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$" always true, ...
2
votes
0answers
82 views

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-...
1
vote
0answers
61 views

Demand Elasticity, Factor Substitution: Independent?

Given $ Y=f(K,L;\sigma) $, the effect on labor from a change in the price of capital can be gauged through a substitution effect and a scale effect: \begin{align*} \frac{\partial L}{\partial r} & ...
2
votes
1answer
90 views

Wages, capital: Substitution and Output Effects

Consider a CES production function $Y=f(K,L)$ with elasticity of factor substitution $\sigma>0$. The substitution effect of higher real wages naturally implies a shift along the isoquant to more $...
4
votes
1answer
67 views

Decision over “max” production function:

I've been presented with the following problem: $$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$ And the objective is to both maximize profit and minimize cost. First of all, if the problems are ...
2
votes
1answer
383 views

Euler's Theorem

Can anyone give me connection and intuition behind each of the following euler's equation- Euler's equation in production function represents that total factor payment equals degree of homogeneity ...
1
vote
1answer
43 views

Quasiconcavity and homogeneity

How to prove that if $f$ is strictly quasi-concave and homogeneous of degree 1, then $f$ is concave? It was left as an exercise by Silberberg & Suen (2001), p.140. I simply could not elaborate ...
1
vote
2answers
28 views

2 firms production decision for one agent

I'm trying to solve the optimal production $\{x,y\}$ for a risk neutral agent with weight $w$ in firm $X$ and weight $1-w$ in firm $Y$. Each firm has marginal cost $c^X$ and $c^Y$ respectively. The ...
0
votes
1answer
63 views

General Equilibrium with Linear Production

I don't think I understand how optimization problems with a linear function work as of now. If you have a production economy with two agents, two goods and Cobb-Douglas utility representation, and you ...
0
votes
1answer
25 views

Price Derivation in a Production Function

Here is a composite goods production function: And here is the price ratio of Ys and Yg, derived from their marginal products: Then the author normalized the price of final goods Y to 1 and somehow ...
1
vote
1answer
156 views

Nested CES Production Function

If I have four input factors (a, b, c, b) and I want to construct a nested CES production function such that (a, b) are substitutes, (c, d) are substitutes and [(a, b), (c, d)] are complements, I.e. a,...
0
votes
1answer
44 views

intuitive interpretation of the marginal return/productivity of capital being less than one

Let's assume you have a production function, f, and you want to know how the output changes with respect to capital, everything else constant (ceteris paribus), so you want to know the marginal ...
4
votes
1answer
64 views

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 ...
3
votes
2answers
62 views

Is there an economic interpretation of the production transformation function?

The production set has a simple meaning: It is the set of all production vectors that are feasible to a firm. The production function also has a simple meaning: It gives the output quantity for a ...
1
vote
2answers
254 views

Question on returns of scale in isoquants

What does the dotted line in the diagram show and what are they called? I am also wondering why the steepness of the isoquants changes at Q=3 for the third diagram. Thanks
-2
votes
2answers
106 views

Production function question

Some help with this would be appreciated.
0
votes
2answers
626 views

Perfect complement graph and isoquant

$f(x_1,x_2) = min \{x_1,x_2\} + x_2$ if that was the production, what would the isoquant be? Would it simply follow $x_1 = x_2$? I'm not entirely sure what it the graph would look like.
0
votes
1answer
222 views

Partial production function question

Hi everyone, I am learning about the partial production function. I don't understand why a tangent it drawn next to the curve; I get that it shows the MPL. Does this mean diminishing marginal product ...
1
vote
1answer
46 views

Estimating production functions with time series data

A while back I asked How do we estimate production functions? The answers given address cases when dealing with cross-sectional data, However most of the data I've been seeing is given by a time ...
4
votes
1answer
65 views

Impact of Natural Disaster on Production Function

Say a natural disaster strikes. People were killed but the losses were small relative to the size of the work force. However, many buildings and infrastructures have been severely damaged. I'm ...
1
vote
2answers
571 views

Is it constant returns to scale if the output of a production function is purely a function of one variable?

For $Y=F(K,L)= 2L$ If I multiply them by an constant $z$: $Y= F(zK,zL0)$, i'll get $2(zL) = z(2L)$. Inputs increase proportionally therefore constant returns to scale. This doesnt seem right ...
0
votes
1answer
27 views

How does hedging using futures work?

I can't understand how it makes sense. From what I've read, corn producers (for example) sell their corn at current price but deliver the corn later, in order to protect themselves from decline in ...
1
vote
0answers
124 views

Estimating Endogenous vs Exogenous growth models

Exogenous economic growth models (mostly those that take technological progress, or change in TFP as exogenous and random) are rather easy to estimate econometrically. But how about endogenous ...
1
vote
0answers
57 views

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 ...
2
votes
1answer
72 views

Choosing Data for CES Production Function

So I am currently trying to write a paper estimating the Constant Elasticity of Substitution Production Function of the USA. I am using the simple version with two inputs capital and labour. Since the ...
1
vote
0answers
39 views

How change in technology affects the price of labour and capital?

If the technology improves how does the price of labour and capital change. We take the neo-classical assumption that demand for each factor depends on it's marginal productivity, and demand and ...
4
votes
1answer
100 views

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. ...
2
votes
1answer
610 views

How was the CES production function derived?

The Constant Elasticity of Substitution production function is defined as: (Taken from Wikipedia) $$Q=F \boldsymbol{\cdot}\left(a\boldsymbol{\cdot}K^r+(1-a)\boldsymbol{\cdot}L^r \right)^{1\over{r}}$$...
4
votes
1answer
52 views

Aggregate production function, factor shares and cointegration

When estimating an aggregate production function you fit your data to a selected functional form of the production function, derive the parameters and inference from there. My question is, is there ...
0
votes
1answer
59 views

Anything written on the process behind “multiplicative” production function?

Intuitively, one might make a naive first guess that the production function of the economy, or of a firm, should be a "leontief" production function: "for example, you need both a factory and a ...
6
votes
1answer
61 views

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 ...