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 ...
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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 ...
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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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2 votes
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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 ...
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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 ...
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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 ...
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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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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 $r$ ...
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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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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} ...
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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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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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For the cost function question (equation in image), I have found TVC as AVC*P. However the MC curve derived is giving imaginary number solution

For the cost function question (equation in image), I have found TVC as AVC*P. However MC curve is showing an imaginary number as solution.
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What's the difference between fixed and variable O&M costs in power generation

Not sure what the difference is btwn Fixed and variable O&M costs. As you can see in this screenshot, both contain maintenance cost. While fixed o&m contains regular and irregular maintenance ...
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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{...
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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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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.
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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 ...
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