# Questions tagged [cost-functions]

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### 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) ...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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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### 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 ...
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### Deriving long-run cost function

I'm a bit unsure about how to derive a long-run cost function. Suppose my production function was $X(L, K)=L^a K^b$, where $a+b>1$. I'm thinking about doing the following, but I'm not sure it's ...
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### 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. ...
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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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### 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 ...
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### 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 ...
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### what results can be derived from the average cost curve?

What is the practical use of knowing a firms average cost curve? The reason why I ask is because computational problems that a firm faces are either with regards profit maximization or cost ...
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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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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 $$TC(y) = \left\{ \begin{... • 61 2 votes 2 answers 672 views ### Creating non-linear cost functions From what I understand, the basic cost function looks like$$C(x_i)=\sum_{i=1}^{n}w_ix_iWhat I'm wondering is whether or not its possible to create a non-linear cost function which adjusts based ... • 7,685 2 votes 2 answers 147 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 ... • 3,414 2 votes 1 answer 97 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 ... • 299 2 votes 3 answers 152 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 1 answer 94 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 ... • 21 2 votes 2 answers 201 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 2 answers 1k 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 ... • 103 2 votes 0 answers 26 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 ... 2 votes 0 answers 56 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)... • 2,021 2 votes 1 answer 66 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 42 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 2 votes 0 answers 257 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 ... • 199 2 votes 0 answers 77 views ### 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 ... • 7,685 2 votes 0 answers 1k views ### 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 ... 2 votes 1 answer 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 ... • 657 1 vote 1 answer 82 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 1 vote 2 answers 237 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, ... • 11 1 vote 2 answers 366 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 1 answer 67 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: ... 1 vote 1 answer 1k 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? • 13 1 vote 0 answers 93 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 ... 1 vote 1 answer 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 ... • 13 1 vote 0 answers 37 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 ... • 11 1 vote 0 answers 160 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} ... • 131 1 vote 0 answers 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 ... • 11 1 vote 2 answers 521 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 0 answers 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} & ... 0 votes 3 answers 2k views ### Is it possible to have constant marginal cost and decreasing average cost simultaneously? [closed] I thought about possibility of occurring such event in the case of presence of fixed costs, but I would like to know others opinions. • 37 0 votes 1 answer 51 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 ... • 21 0 votes 3 answers 94 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 1 answer 364 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{\... 0 votes 1 answer 81 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? 0 votes 1 answer 73 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 ... • 1,040 0 votes 1 answer 3k 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$$. The factor prices are w_1=4 and w_2=3. Calculate the company's supply function. Q2: A company's cost function is$$...
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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 ...