Questions tagged [cost-functions]
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57
questions
0
votes
1answer
43 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 ...
2
votes
2answers
100 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 ...
0
votes
0answers
31 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
$$
C = 0.1{...
2
votes
1answer
78 views
Finding production given total cost (shephard's lemma)
Given a total cost function, for example,
$$ 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 ...
0
votes
0answers
22 views
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$,...
0
votes
0answers
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.
4
votes
1answer
65 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. ...
2
votes
1answer
43 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 ...
2
votes
0answers
39 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 ...
12
votes
6answers
3k 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) ...
1
vote
1answer
72 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!
0
votes
3answers
82 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?
0
votes
0answers
54 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 ...
1
vote
0answers
83 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
1answer
405 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
vote
1answer
31 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 ...
3
votes
2answers
361 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
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
5
votes
1answer
267 views
CobbDouglas: Constant marginal costs and constant returns to scale
A company has a production function:
$$y=x_1^{\alpha}x_2^{1-\alpha}$$
where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its ...
5
votes
0answers
58 views
Constant returns to scale and cost function: $C(p,ty) = tC(p,y)$
How can I prove that for a production function $F:\mathbb X \rightarrow \mathbb R$ with constant returns to scale
$$\forall x\in \mathbb X, \forall t > 0: \ \ F(tx) = t F(x)$$
and with the cost ...
2
votes
1answer
475 views
Cost function from CES production function
How can I find the cost function $c(w,p)$ given that the production is
$$ 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{...
3
votes
2answers
585 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 ...
0
votes
1answer
289 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{\...
1
vote
0answers
33 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 ...
0
votes
1answer
2k 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
$$...
0
votes
1answer
78 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?
7
votes
3answers
752 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
1answer
65 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
0answers
210 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 ...
0
votes
1answer
62 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 ...
0
votes
1answer
22 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,...
6
votes
1answer
608 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 ...
0
votes
1answer
57 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 ...
0
votes
0answers
30 views
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 ...
1
vote
2answers
331 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 ...
1
vote
2answers
190 views
What does "r" represent in the total cost function?
I know that the total cost function of a firm in the short run is:
TC = wL + rK,
where rK is essentially a constant. I understand the variables w, L and K, but I still don't get what r is. I mean, ...
1
vote
0answers
149 views
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} ...
2
votes
1answer
86 views
Short Run Total Cost function Question
I am confused about the Short Run Total Cost function of this problem.
If the firm's production function is $F(K,L) = K+\ln(L)$ derive the short run total cost function.
I was able to solve the ...
2
votes
2answers
196 views
Optimal Production Input in Relation to Cost Minimization Problem
I was doing my homework and got really confused about how to approach the optimal levels of inputs when there are three variables. My current understanding is that the problem is to solve the ...
2
votes
2answers
975 views
Why is the price of capital ‘r’ ? (From Cost function)
according to the Cost formula in microeconomics class,
Total Fixed Cost is represented as “rK” (K as in unchanging, fixed K)
now my economics teacher tells me this ‘r’ is the interest rate at which ...
0
votes
1answer
44 views
Production function involving profit maximisation
Hi, I don't get how the answer of d is deduced in this question because I don't think I made any mistakes in my calculation and have also used all the information given. After knowing L is 800, I ...
0
votes
1answer
19 views
Trade cost on Endowment model
I think in real endowment model, if there's trade cost as 't', then the MRS should be really small or large to make a consumer trade his endowment goods. Is there any model include this trade cost or ...
1
vote
0answers
29 views
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 ...
1
vote
2answers
490 views
Derive the cost function for a Homothetic production function
I'm having trouble understanding the steps in showing that a Homothetic production function's cost function must be expressible in the form $C(w, q) = a(w)b(q)$.
Since the production function is ...
1
vote
1answer
974 views
Coefficients of Cubic Total Cost Function
Given a Total Cost equation $TC(Q) = a + bQ + cQ^2 + dQ^3$ what do the coefficients mean? For example $a$ is fixed costs, what are $b,c,d$ and how are they calculated?
3
votes
0answers
3k views
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 ...
2
votes
3answers
146 views
Is "$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$" always true?
For the productions $f(k,l) $ that are continuously differentiable, is the proposition that
"$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$"
always true, I have ...
2
votes
1answer
3k views
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 ...
1
vote
0answers
75 views
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} & ...
4
votes
1answer
380 views
Decision over "max" production function:
I've been presented with the following problem:
$$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$
And the objective is to both maximize profit and minimize cost. First of all, if the problems are ...
3
votes
1answer
3k views
Prove all cost functions are concave in input prices and demand for inputs is downward
I've seen proofs that cost functions are concave of the form
$C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$
although this neither feels convincing nor does it seem like a ...
