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.

Filter by
Sorted by
Tagged with
0
votes
0answers
20 views

Production for multiplant firm?

A multi-plant firm will never produce at a plant with an increasing marginal cost when they own another plant with a decreasing marginal cost. Is this true? My reasoning behind this is that firms ...
0
votes
1answer
32 views

When will the reserves be exhausted?

A rough estimate of the oil and gas reserves in some country at the beginning of 2010 was 15 billion tons. production that year was approximately 250 million tons. when will the reserves be exhausted ...
0
votes
1answer
56 views

How to prove that profit function is convex in price (with smaller price)?

According to this site, if output price increases from $p*$ to $p'$ and factor prices remain constant, then a new production bundle chosen must yield at least the same amount of profits as the old ...
0
votes
1answer
46 views

How to prove that a concave production imply that the input requirement sets are convex?

According to page 7 of this slide, "A convex production set Y implies that the associated input requirement set V(y) is convex". How can one go about proving it?
1
vote
0answers
36 views

Log differentiation of aggregate production function [closed]

Suppose we have an aggregate production function $Y = A F(K, L)$. I'm following some slides which then states that we if log differentiate we get the following: $\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} +...
2
votes
1answer
42 views

The Household Production Function

I was wondering whether someone can explain the household production function. Specifically, the variant presented in Patanayak et al 2005. The paper uses the HPF to determine household willingness to ...
2
votes
1answer
56 views

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 ...
-1
votes
1answer
23 views

Production technology of $y=2x$

I have a given product $y$ that is produced by the input $x$ in the following relation: $2x=y$. In our example, we are given the unit price of $x$ is $16$. Find the unit cost of $y$. The answer is $8$....
1
vote
1answer
79 views

Why is the price of capital ‘r’ ? (From Cost function)

according to the Cost formula in microeconomics class, Total Fixed Cost is represented as “rK” (K as in unchanging, fixed K) now my economics teacher tells me this ‘r’ is the interest rate at which ...
0
votes
0answers
44 views

Production technology and efficiency

I have been practicing some questions on production function and efficiency and I came across the following questions. For question 1 what I did is, the efficiency of firm A in q1 = production of ...
0
votes
0answers
12 views

Stochastic frontier analysis in a unit out put production function. Taking logs is causing issues?

I wish to perform stochastic frontier analysis to calculate inefficiency of firms, but for a unit output isoquant ( imp) now y'=1, k'=k/y and l'=l/k. Now, these values lie between 0 and 1 (including 0)...
0
votes
1answer
46 views

Can a CES parameter be negative?

I estimated the CES function (https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) using national accounts data for France. I got (using notation in wikipedia): a = 1.19 r = -0.48 so ...
2
votes
1answer
43 views

Continuity of Prices for Constant Elasticity of Substitution Production Functions

Imagine I have a CES production function $$ Y_{\sigma} = Z [ \sum_{i=1}^N \alpha_{i} X_i^{\frac{\sigma}{1-\sigma}}]^{\frac{1-\sigma}{\sigma}}$$ I know that as $\sigma \to 1$, the corresponding ...
0
votes
1answer
38 views

Production function involving profit maximisation

​Hi, I don't get how the answer of d is deduced in this question because I don't think I made any mistakes in my calculation and have also used all the information given. After knowing L is 800, I ...
-1
votes
1answer
51 views

MRTS question involving production function [closed]

My work out shows constant MRTS and also increasing returns to scale. I thought the answer was C as I only found increasing marginal products of labour and capital. I really don't see how the answer ...
2
votes
1answer
202 views

CES production function profit and supply function

I need to derive the profit function for the following CES function: $$ f(z) = (\sqrt{z_{1}^{\rho} + z_{2}^{\rho}})^{1/ \rho}$$ where $\rho \leq 1$. This is the answer that I am supposed to be getting:...
0
votes
1answer
60 views

Decreasing and increasing returns to scale question

Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d ...
-1
votes
1answer
46 views

Keynesian-cross analysis [closed]

I have a question from my textbook which is: Using the Keynesian-cross analysis, assume that the consumption function is given by C = 100 + 0.6(Y – T). If planned investment is 100 and T is 100, then ...
2
votes
0answers
55 views

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 ...
1
vote
0answers
15 views

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 ...
3
votes
0answers
41 views

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 ...
1
vote
0answers
131 views

What is the difference between imperfect substitutes and complements in a production function?

According to the following definition: ...
2
votes
0answers
136 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
237 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
80 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
3answers
329 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
162 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
133 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
436 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
58 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
208 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 ...
6
votes
2answers
794 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
92 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
243 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
58 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
119 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
105 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
48 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
123 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 ...
3
votes
0answers
1k 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 ...
3
votes
3answers
116 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, I have ...
2
votes
0answers
175 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
72 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
118 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
109 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 ...
3
votes
1answer
887 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
64 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
30 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 ...
1
vote
1answer
103 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
31 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 ...