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Questions tagged [cost-functions]

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0
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1answer
21 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, ...
1
vote
1answer
22 views

Supply curve when the marginal cost is zero

The supply curve is built as the average marginal cost (MC), when the MC is equal or higher than the average cost (AC) The marginal cost increases, as a result of the opposite effect of marginal ...
1
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0answers
54 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} & ...
4
votes
1answer
55 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 ...
1
vote
1answer
181 views

Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
3
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2answers
75 views

what results can be derived from the average cost curve?

What is the practical use of knowing a firms average cost curve? The reason why I ask is because computational problems that a firm faces are either with regards profit maximization or cost ...
2
votes
0answers
38 views

Econometrically estimating the Leontief cost function

in general the Leontief cost function is represented as: $$c(w,y)=y\sum_{i=1}^kw_ix_i$$ where: $$y=\min\left[{\frac{x_1}{\alpha_1},...,\frac{x_n}{\alpha_n}}\right]$$ How does one go about ...
4
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0answers
87 views

Understanding the Diewertt Cost Function

The Diewert cost function (as described in Microeconomic Analysis by Hal Varian 3rd Edition) takes the form of: $$c(w,y)=y\sum_{i=1}^k\sum_{j=1}^kb_{ij}\sqrt{w_iw_j}$$ Varian goes on to say (page ...
2
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0answers
307 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 ...
3
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1answer
621 views

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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3answers
528 views

Is it possible to have constant marginal cost and decreasing average cost simultaneously? [closed]

I thought about possibility of occurring such event in the case of presence of fixed costs, but I would like to know others opinions.
2
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2answers
160 views

Creating non-linear cost functions

From what I understand, the basic cost function looks like $$C(x_i)=\sum_{i=1}^{n}w_ix_i$$ What I'm wondering is whether or not its possible to create a non-linear cost function which adjusts based ...