# 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 ...
• 165
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### 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 ...
• 7,685
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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 ...
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### Cost function related question

I am doing this practice problem for my exam: The question says: an industry consists of a large number of firms, each of which has a cost function of the form: $c(w_1,w_2,q)=(q^2+1)w_1+(q^2+2)w_2$ ...
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### Solving Cost Minimization with CES Production Function and Two Types of Input

A CES aggregator: $y=\left(\int_{0}^{1} y(i)^{\frac{\eta-1}{\eta}} d i\right)^{\frac{\eta}{\eta-1}}$, where $i \in[0,1]$. For each intermediate good: $y(i)=\ell_{r}(i)+\ell_{c}(i) / a(i)$, where $a(i)$...
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### 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
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### 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 ...
• 199
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### 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 ...
• 7,685
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### 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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### 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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1 vote
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### 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 vote
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### 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 ...
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1 vote
160 views