Questions tagged [cost-functions]
The cost-functions tag has no usage guidance.
73 questions
1
vote
2
answers
43
views
Why is supply equal to the MC curve for firms
As far as I know, we view the supply curve for a firm as the MC curve, of course, firms would want to produce at the profit maximising point but say they had to produce amounts below and or above this ...
- 95
1
vote
1
answer
54
views
Can the Average Cost Curve have a different shape other than U?
I'm a Computer Science undergraduate taking Microeconomics for my final exam. I've been studying the concept of average cost. I've always understood that the average cost curve is typically U-shaped ...
- 13
9
votes
3
answers
1k
views
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 ...
- 371
0
votes
1
answer
44
views
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
1
answer
111
views
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 ...
- 11
1
vote
2
answers
362
views
How to derive the short run cost function
Given the production function $f(K, L)=\min\{3K,2L\}$, the procedure to find the long-run cost function would be to use the condition: $3K=2L=Y$ where $K=\frac{\overline{Y}}{3}$ and $L=\frac{\overline{...
- 45
2
votes
1
answer
60
views
Inappropriate use of Calculus in estimating ΔCost?
I have the following model, and i solve for my optimised conditional factor demands, and minimised cost functions $C$. (Note: I have turned a minimisation problem into a maximisation problem). Let's ...
- 1,011
2
votes
0
answers
18
views
Conditions on turnover as a function of number of sales to be a concave function
Suppose I have a customer base of size 100. An arbitrary customer has a private valuation for my product, which shall be represented by the random variable $X$. (Suppose $X$ takes on values between $0$...
- 121
2
votes
1
answer
256
views
Quasi-convex constraints using monotonic functions
I believe i have a major misunderstanding surrounding quasi-convex constraints in maximisation, when using monotone functions. Can you help me spot my errors please?
The definition of a quasi-convex ...
- 1,011
2
votes
0
answers
150
views
Derivation of Allen-Uzawa Elasticity of Substitution from Hicks Elasticity of Substitution in two goods
Everywhere I've looked, the author of the text asserts that the Allen-Uzawa Elasticity of Substitution is equal to the Hicks Elasticity of Substitution in two goods. I've spent a long time trying to ...
- 121
2
votes
1
answer
308
views
Why does the LRAC (long-run average cost) curve intersect with the SRAC (short-run average cost) curve at exactly one point?
Why does the LRAC (long-run average cost) curve intersect with the SRAC (short-run average cost) curve at exactly one point? I understand why there's at least one intersection (it's because, given an ...
- 366
1
vote
1
answer
304
views
Where does the short-run and long-run costs intersect if $k$ is fixed?
Suppose the short-run cost function is written as $SC(\bar{w}, \bar{r}, y, k)$ and the long-run cost function as $C(\bar{w},\bar{r},y)$ where the rates $w$ and $r$ are fixed. $y$ determines the ...
- 366
1
vote
0
answers
69
views
Finding cost function
The production function is as follows
$$f(z)=(z_1+z_2)(z_3+z_4)$$
Find the cost function?
What I did is as follows. But I am not sure about my solution. How do you solve it?
*duplicated question
- 192
0
votes
1
answer
43
views
How is production managed with respect to the long run vs the short run?
Assuming perfect competition, I think that firms are price takers in the labor/capital markets as well (in the short and long run), correct?
And I know that the Long-run total cost curve is derived by ...
- 61
0
votes
1
answer
34
views
Different types of cost functions (curves)
I see three types of cost functions:
$C(q) = 4q$ where $q$ is the quantity
$C(w_1, w_2 ,q) = w_1w_2q$ where $w_1, w_2$ are the rental rates and $q$ is the quantity of the product
$C(\mathbf{w}, \...
- 15
1
vote
0
answers
36
views
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 $c(w,r,q) = w^{0.4}r^{0.6}q$, ...
- 11
2
votes
0
answers
217
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 $P_3/P_4<1/2$
...
- 192
2
votes
0
answers
38
views
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: $c(w_1,w_2,q)=(q^2+1)w_1+(q^2+2)w_2$ ...
- 21
0
votes
1
answer
523
views
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 $z_1$ ...
- 1,048
2
votes
0
answers
415
views
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 $a(i)$...
- 2,516
0
votes
1
answer
173
views
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 ...
- 31
2
votes
2
answers
2k
views
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 ...
- 3,494
1
vote
1
answer
76
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
$$
C = 0.1{...
- 309
2
votes
1
answer
753
views
Finding production given total cost (shephard's lemma)
Given a total cost function, for example,
$$ C = q {w}^{3/4}{v}^{1/4}
$$
and Shephard's Lemma, how do you find the underlying production function $q(k,l)$?
For this example, Shephard's Lemma provides ...
- 309
4
votes
1
answer
361
views
Solving the following cost minimization problem using Kuhn-Tucker conditions
I am currently getting my Masters in Economics. I did not get any exposure to optimization with inequality constraints in my undergrad. I would like to ensure that I am doing this problem correctly. ...
- 103
2
votes
1
answer
389
views
How is the translog cost function derived?
I realize that the translog production function is derived as a second order taylor approximation of a production function (e.g. the CES-production function), as explained in this post.
Is the ...
- 23
2
votes
0
answers
63
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 ...
- 497
12
votes
6
answers
7k
views
Why are cost functions often assumed to be convex in microeconomics?
Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics?
For me this goes against the intuition of economies of scale. There are fixed costs (FC) ...
- 2,611
1
vote
1
answer
146
views
Trigonometric Cost Function [duplicate]
I've been reading on producer theory and came up with a ridiculous question. Has anyone tried to model costs with a trigonometric function? would it work with the assumptions we need? Thanks!
- 13
0
votes
3
answers
231
views
Why min AC = min SRAC at the minima of AC curve?
At the lowest point of long run average cost curve AC, the SAC is also at its minimum and that is not the case with any other SAC curve bounded by the envelope. Why is that?
- 99
1
vote
0
answers
246
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$ ...
-2
votes
1
answer
2k
views
Determine marginal revenue given demand curve and marginal cost
a)Determine marginal revenue curve if firm can only charge 1 price,List demand curve,marginal revenue curve,,marginal cost,average total cost equations.
b)What is optimal price and quantity?
c)If firm ...
- 1
1
vote
1
answer
37
views
Second Order Derivatives in Becker's Crime and Punishment
I'm trying to understand Becker's seminal paper Crime and Punishment (1968) particularly the parameter of cost of apprehension and conviction and their second order partial derivatives.
The paper ...
- 13
3
votes
2
answers
843
views
Under what condition is a cost function strictly concave in prices?
Define the unit cost function as
$$
c(w) = \min_{z\geq 0} w\cdot z
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
- 168
5
votes
1
answer
1k
views
CobbDouglas: Constant marginal costs and constant returns to scale
A company has a production function:
$$y=x_1^{\alpha}x_2^{1-\alpha}$$
where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its ...
- 175
5
votes
0
answers
315
views
Constant returns to scale and cost function: $C(p,ty) = tC(p,y)$
How can I prove that for a production function $F:\mathbb X \rightarrow \mathbb R$ with constant returns to scale
$$\forall x\in \mathbb X, \forall t > 0: \ \ F(tx) = t F(x)$$
and with the cost ...
- 165
2
votes
1
answer
4k
views
Cost function from CES production function
How can I find the cost function $c(w,p)$ given that the production is
$$ f(x)=(x_1^p + x_2^p)^{1/p} \ \ for\ \ 0<p <1 $$
I tried to solve it and found that
$$TC(y) = \left\{
\begin{...
- 61
5
votes
2
answers
4k
views
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 ...
- 305
0
votes
1
answer
2k
views
Marginal cost given (Cobb-Douglas) production
My function is $y=x_1^\alpha x_2^\beta$ with $\beta={1-\alpha}$.
I found: the minimization problem for demand to be
$x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\frac{\alpha}{\beta} \right )^{\frac{\...
user31331
1
vote
0
answers
73
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 ...
- 111
0
votes
1
answer
9k
views
Calculate supply function based on production or cost function
Q1: A company has the following production function:
$$f(x_1,x_2) = 2x_1 + x_2$$.
The factor prices are $w_1=4$ and $w_2=3$. Calculate the company's supply function.
Q2: A company's cost function is
$$...
- 13
0
votes
1
answer
140
views
How to calculate the minimun of Average Fixed Cost knowing the Average Fixed Cost [closed]
Given the Average Fixed Cost, how does one calculate its minimum?
- 11
7
votes
3
answers
970
views
Long Term Economic Profit for Perfectly Competitive market
When we consider a perfectly competitive market, in the short run we will run a firm if the total economic profit though negative till price is above shutdown point.In long run we will run at an ...
1
vote
1
answer
80
views
Interpretation of $x c '(x)$
Consider a cost function that is continuous, differentiable and (possibly) convex: $c(x):\mathbb{R}^+\to \mathbb{R}$. I was wondering if there is a "common" way to interpret the expression:
$...
2
votes
0
answers
716
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 ...
- 319
0
votes
1
answer
111
views
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 ...
- 189
0
votes
1
answer
28
views
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,...
- 103
6
votes
1
answer
626
views
Fixed cost of a firm
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 ...
- 73
0
votes
1
answer
82
views
Is the minimum of short run average cost equal to the minimum of long run average cost? [duplicate]
I understand that for perfect competition, the price is equal to minimum short and long run average cost in the long run as there cannot be any supernormal profits.
Does this mean that the short run ...
1
vote
2
answers
949
views
Does the minimum of short-run average cost equal the minimum of long-run average cost in the long run for perfect competition?
I was recently reading this resource (http://www2.econ.iastate.edu/classes/econ101/hallam/Comp_LongRun_HND.pdf) which states that in the long run for perfect competition, price is equal to both the ...
- 191