Questions tagged [cost-functions]

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Constant returns to scale and cost function: $C(p,ty) = tC(p,y)$

How can I prove that for a production function $F:\mathbb X \rightarrow \mathbb R$ with constant returns to scale $$\forall x\in \mathbb X, \forall t > 0: \ \ F(tx) = t F(x)$$ and with the cost ...
4
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0answers
147 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 ...
3
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0answers
3k 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 ...
2
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0answers
39 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 ...
2
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0answers
210 views

Exponential cost function (of effort) and something else

Consider a two-player model with P and A. A can engage in criminal activities and P can catch that by putting effort into it. The more effort P puts into it, the more likely he's going to catch the ...
2
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0answers
77 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 ...
2
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0answers
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 ...
2
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1answer
3k 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
83 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 $r$ ...
1
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0answers
33 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 ...
1
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0answers
149 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} ...
1
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0answers
29 views

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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75 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} & ...
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31 views

Maximizing profit with a simple probabilistic production function (basic practice problem)

A restaurant finds that less orders for their soup of the day are placed on warmer days so they discount the usual 7USD price to 5USD on warmer days. The cost of making the soup is given by $$ C = 0.1{...
0
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22 views

Market equilibrium when marginal cost is decreasing

I'm trying to solve this problem: Technology for producing $q$ gives rise to the cost function $c(q) = aq + bq^2$. The market demand for $q$ is $p = \alpha - \beta q$ (a) If $a > 0$, if $b < 0$,...
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17 views

Is there a publication containing detailed cost and fuel usage functions for automobiles?

I want something that will take the elevation, fuel tank level, load/weight, road grade, etc and give me an instantaneous fuel burn value.
0
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30 views

Is optimizing revenue and expense objectives simultaneously better than optimizing profit as composite objective?

In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I ...