Questions tagged [cost-functions]
The cost-functions tag has no usage guidance.
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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 $0$...
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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 ...
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Does decreasing a player's external regret always (monotonically?) decrease that player's cost function?
In a game in which, at each time step, a player declares a mixed strategy, then an adversary assigns a cost to each of that player's pure strategies, and then the mixed strategy is applied and that ...
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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, \...
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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 ...
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Income elasticities of demand in the Transcendental Log Cost model
I just wanted to ask a questions about the Translog Model that might be silly, but I come from a totally different background (please bear with me)... To avoid confusion, I will be following notation ...
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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 ...
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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 ...
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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
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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 ...
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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}, \...
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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 $c(w,r,q) = w^{0.4}r^{0.6}q$, ...
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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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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
$$
C = 0.1{...
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Finding production given total cost (shephard's lemma)
Given a total cost function, for example,
$$ 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 ...
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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.
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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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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 ...
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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 ...
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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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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!
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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?
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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 ...
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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$ ...
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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 ...
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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 ...
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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
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
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CobbDouglas: Constant marginal costs and constant returns to scale
A company has a production function:
$$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)$$
and with the cost ...
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Cost function from CES production function
How can I find the cost function $c(w,p)$ given that the production is
$$ 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{...
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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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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
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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 ...
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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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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?
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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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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:
$...
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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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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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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 ...
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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 ...
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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 ...
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