All Questions
Tagged with production-function cost-functions
26 questions
0
votes
1
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43
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How is production managed with respect to the long run vs the short run?
Assuming perfect competition, I think that firms are price takers in the labor/capital markets as well (in the short and long run), correct?
And I know that the Long-run total cost curve is derived by ...
- 61
2
votes
0
answers
217
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 $P_3/P_4<1/2$
...
- 192
0
votes
1
answer
523
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isoquant of a leontief production function
Consider a firm that can produce q units of good G using two technologies and two production factors, $z_1$ and $z_2$. There are two ways how a firm
can produce the good G: It can use 2 units of $z_1$ ...
- 1,048
0
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1
answer
173
views
How do you convert or move from a linear cost function to a quadratic cost function?
I am reading a book on electricity cost modelling. I understand equation 2.7 below, which indicates that the total cost for an ith plant is a function of fixed cost(FC), fuel cost(FL), plant ...
- 31
2
votes
1
answer
753
views
Finding production given total cost (shephard's lemma)
Given a total cost function, for example,
$$ C = q {w}^{3/4}{v}^{1/4}
$$
and Shephard's Lemma, how do you find the underlying production function $q(k,l)$?
For this example, Shephard's Lemma provides ...
- 309
2
votes
1
answer
389
views
How is the translog cost function derived?
I realize that the translog production function is derived as a second order taylor approximation of a production function (e.g. the CES-production function), as explained in this post.
Is the ...
- 23
2
votes
0
answers
63
views
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
1
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0
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246
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 $r$ ...
3
votes
2
answers
843
views
Under what condition is a cost function strictly concave in prices?
Define the unit cost function as
$$
c(w) = \min_{z\geq 0} w\cdot z
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
- 168
5
votes
1
answer
1k
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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 ...
- 175
5
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2
answers
4k
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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 ...
- 305
0
votes
1
answer
2k
views
Marginal cost given (Cobb-Douglas) production
My function is $y=x_1^\alpha x_2^\beta$ with $\beta={1-\alpha}$.
I found: the minimization problem for demand to be
$x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\frac{\alpha}{\beta} \right )^{\frac{\...
user31331
1
vote
0
answers
73
views
How to explain the flattening of the SRAC curve?
I discovered that there is a way that Short-run average cost curve could become 'flatter' instead of shifting. Yet I cannot find an explanation of why and how it can become flatter.
For example, in ...
- 111
0
votes
1
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9k
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Calculate supply function based on production or cost function
Q1: A company has the following production function:
$$f(x_1,x_2) = 2x_1 + x_2$$.
The factor prices are $w_1=4$ and $w_2=3$. Calculate the company's supply function.
Q2: A company's cost function is
$$...
- 13
1
vote
1
answer
80
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Interpretation of $x c '(x)$
Consider a cost function that is continuous, differentiable and (possibly) convex: $c(x):\mathbb{R}^+\to \mathbb{R}$. I was wondering if there is a "common" way to interpret the expression:
$...
0
votes
1
answer
111
views
Revenues and cost functions
Let's assume that there is a firm that produces a single good, $q=f(x)$, where $x$ is a single input. The firm can sell it on the market at a price $p$. It's production cost is given by a cost ...
- 189
1
vote
0
answers
282
views
Kuhn-Tucker conditions in linear cost minimization
Suppose we have the production function $f: \mathbb{R}^{2} \to \mathbb{R}$ given by
$$
f(x,y) = ax + by
$$
and input prices $p_{1}$ and $p_{2}$, and we want to minimize the cost function $p_{1}x_{1} ...
- 131
2
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2
answers
2k
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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 ...
- 105
1
vote
1
answer
81
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 ...
- 15
1
vote
2
answers
764
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 ...
- 43
3
votes
0
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4k
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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 ...
- 31
2
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3
answers
278
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 ...
- 123
1
vote
0
answers
80
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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} & ...
- 51
4
votes
2
answers
751
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 ...
- 51
2
votes
0
answers
1k
views
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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4
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1
answer
7k
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Deriving long-run cost function
I'm a bit unsure about how to derive a long-run cost function. Suppose my production function was $X(L, K)=L^a K^b$, where $a+b>1$.
I'm thinking about doing the following, but I'm not sure it's ...
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