Questions tagged [cost-functions]
The cost-functions tag has no usage guidance.
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Efficient Scale is necessarily equal to zero if $MgC(q=0) >$ Fixed Cost?
Assume the marginal cost is strictly increasing and always larger than the fixed cost - in particular, at $q=0$ (no production). Does it imply that the efficient scale is equal to zero? (Define ...
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2answers
58 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 ...
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1answer
40 views
Coefficients of Cubic Total Cost Function
Given a Total Cost equation $TC(Q) = a + bQ + cQ^2 + dQ^3$ what do the coefficients mean? For example $a$ is fixed costs, what are $b,c,d$ and how are they calculated?
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322 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 ...
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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
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1answer
206 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 ...
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0answers
57 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
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1answer
66 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
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1answer
462 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
96 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 ...
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0answers
43 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 ...
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0answers
96 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 ...
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0answers
530 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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1answer
1k 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
908 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.
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2answers
222 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 ...
