# Questions tagged [cost-functions]

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### Cost Minimization and Karush-Kuhn-Tucker

A firm produces an output $y$ using two inputs $x_1$ and $x_2$, where the production function is given by $y = \sqrt{x_1 x_2}$ for any $(x_1, x_2) \in \mathbb{R}^2_+$. Union agreements obligate the ...
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### To find optimal number of customers in fully competitive market with both MC and AC increasing?

This graph indicates Marginal cost (MC) and Average cost (AC) curves to obtain customers. AC is increasing because MC is increasing. It is seen that the decreasing return to scale because MC has ...
1 vote
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### Cost function from a weighted CES production function

I want to find the cost function given the CES production function: $$Y = F(x_1,x_2) = (\lambda x_1^ \rho+(1-\lambda)x_2^\rho)^\frac{1}{\rho}$$ with $0<\rho<1$. So far I have set up the ...
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### Is the cost function always of the form $w \cdot x$?

Consider a profit-maximizing (or cost-minimizing) firm with a production function $f(x,y)$. If I am given the inputs $x,y$, the input costs $w,r$ and the cost function $c(w,r,q) = w^{0.4}r^{0.6}q$, ...
149 views

### Find cost function for given production function

I have the following production function $$f(x_1,x_2,x_3,x_4)=max\{\min\{x_1, x_2), x_3+2x_4\}\}\ge q$$ And I want to find the cost function. What I think (1) $P_1+P_2 <P_3$ and $P_3/P_4<1/2$ ...
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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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### 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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### isoquant of a leontief production function

Consider a firm that can produce q units of good G using two technologies and two production factors, $z_1$ and $z_2$. There are two ways how a firm can produce the good G: It can use 2 units of $z_1$ ...
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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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### How do you convert or move from a linear cost function to a quadratic cost function?

I am reading a book on electricity cost modelling. I understand equation 2.7 below, which indicates that the total cost for an ith plant is a function of fixed cost(FC), fuel cost(FL), plant ...
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### Why is MC = ATC the same point for both the breakeven point and an investor maximizing return?

Let $\pi(y) = R(y) - C(y)$ be profits where $R(y)$ is revenue and $C(y)$ is costs. Let $R(y) = p_y y$. Then \begin{align*} \frac{\partial \pi }{\partial y} &= 0\\ \frac{\partial x}{\partial y}(p_y ...
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### What is the returns to scale of the production function q = min {K, L^(1/2)}?

I learned that when there is decreasing returns to scale, the average cost is always increasing. But the professor told us today that the other way around might not always be true. So if average 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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### Revenues and cost functions

Let's assume that there is a firm that produces a single good, $q=f(x)$, where $x$ is a single input. The firm can sell it on the market at a price $p$. It's production cost is given by a cost ...
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### Formula for splitting profit and loss for every person [closed]

I am looking for a formula to calculate even distribution of loss or profit between involved parties. Let's speak with some examples as I feel it will be easier. Example 1 Person 1 Balance: 2,000,...
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Suppose that a firm has a total cost function given by: $TC(q) = \frac{5}{q+1} + 5 + 5q + q^2$. What is the fixed cost? I seem to be able to come up with two "answers", which cannot be correct. My ...