Questions tagged [cost-functions]

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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 ...
fabs's user avatar
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Different estimates from 2SRI and fixed effects regression. is this endogeneity?

I am comparing two different models to resolve potential endogeneity concerns in my empirical models. First, I ran fixed-effects models without handling any endogeneity concerns, and I got significant ...
Sean Park's user avatar
1 vote
2 answers
186 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{...
Debbie's user avatar
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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 ...
CormJack's user avatar
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2 votes
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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 $0$...
willem's user avatar
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2 votes
1 answer
166 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 ...
CormJack's user avatar
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45 views

Cost minimization and then log differentiation

I have trouble deriving the third equation from the second one. The model is in: https://www.nber.org/papers/w30240 The firm's cost minimization problem is as follows: \begin{equation} \min _{L_i, \...
Shcen's user avatar
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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 ...
Andrew Lys's user avatar
2 votes
1 answer
240 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 ...
Rick_Morty's user avatar
1 vote
1 answer
172 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 ...
Rick_Morty's user avatar
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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
studentp's user avatar
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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 ...
user42504's user avatar
0 votes
1 answer
24 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}, \...
Patricia's user avatar
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35 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 $c(w,r,q) = w^{0.4}r^{0.6}q$, ...
bountyhunter's user avatar
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0 answers
122 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.
VAISHAKH NAIR's user avatar
2 votes
0 answers
35 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: $c(w_1,w_2,q)=(q^2+1)w_1+(q^2+2)w_2$ ...
Adam Young's user avatar
0 votes
1 answer
435 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 $z_1$ ...
Maybeline Lee's user avatar
2 votes
0 answers
355 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 $a(i)$...
Alalalalaki's user avatar
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1 answer
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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 ...
od320's user avatar
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2 votes
2 answers
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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 ...
Stan Shunpike's user avatar
1 vote
1 answer
63 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{...
kleinerde's user avatar
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2 votes
1 answer
568 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 ...
kleinerde's user avatar
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0 answers
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.
John Sohn's user avatar
4 votes
1 answer
305 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. ...
Mistah White's user avatar
2 votes
1 answer
280 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 ...
Freddy's user avatar
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0 answers
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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 ...
hrrrrrr5602's user avatar
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) ...
Richard Hardy's user avatar
1 vote
1 answer
130 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!
Tlarre's user avatar
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0 votes
3 answers
188 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?
reasonStore's user avatar
0 votes
0 answers
163 views

Why does LRAC not connect the minima of SRAC curves? [duplicate]

Can anyone please provide an intuitive explanation and proper mathematical reason for non-intersection of SRAC and LRAC at the minimas of SRAC? I am seeing conflicting [1] [2] answers on the site ...
reasonStore's user avatar
1 vote
0 answers
225 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 $r$ ...
DoubleRainbowZ's user avatar
-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 ...
JanusP's user avatar
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1 vote
1 answer
36 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 ...
Ardhi's user avatar
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3 votes
2 answers
769 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 ...
user_lambda's user avatar
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 ...
Lifeni's user avatar
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5 votes
0 answers
271 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 ...
user270396's user avatar
2 votes
1 answer
3k 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{...
victor's user avatar
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5 votes
2 answers
3k 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 ...
Robin311's user avatar
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0 votes
1 answer
1k 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{\...
user avatar
1 vote
0 answers
60 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 ...
brikas's user avatar
  • 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 $$...
jeet31's user avatar
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0 votes
1 answer
125 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?
Alumi's user avatar
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7 votes
3 answers
934 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 ...
santhosh kota's user avatar
1 vote
1 answer
79 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: $...
Weierstraß Ramirez's user avatar
2 votes
0 answers
638 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 ...
Lin Jing's user avatar
  • 319
0 votes
1 answer
106 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 ...
Yorgos's user avatar
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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,...
nass's user avatar
  • 103
6 votes
1 answer
623 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 ...
pc724's user avatar
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0 votes
1 answer
78 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 ...
danielmason's user avatar