Questions tagged [cost-functions]
The cost-functions tag has no usage guidance.
0
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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 ...
0
votes
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
votes
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 ...
