Questions tagged [producer-theory]
Study of the behavior of firms in organizing their production and allocating productive resources.
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Economics of Christmas Trees and Interest Rates
True/False: If Christmas tree growers harvest and market their trees at earlier ages, one possible explanation is that interest rates have fallen.
My Intuition is that the interest rate represents ...
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Why is the demand curve that a perfectly competitive firm faces horizontal while the market demand curve is negatively sloped?
I'm studying producer-theory and I'm stuck on this. Maybe I'm missing something important, but if the demand curve facing a firm in a perfectly competitive market is the same as the market demand ...
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Why free disposal assumption needed in Prop 5.C.1 and 5.C.2 in MWG?
I'm a little confused as why we needs only the assumption of Y being closed and satisfies free disposal in the MWG prop 5.C.1 and 5.C.2. I think i know why Y needs to be closed but what about free ...
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If a production function is homothetic, the MRTS is the ratio of the inputs used. But is the converse also true?
We know that when a production function is homothetic, the MRTS is constant along the ray through the origin (it is a ratio of the inputs used).
But is it true that if the MRTS is ratio of the inputs ...
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How to aggregate goods with different units of measurement to reduce the economy with a Cobb Douglas utility function?
I want to model a economy where consumers have a Cobb Douglas utility function and where X1 = goods that pay a value added TAX (VAT), and X2 = goods that are exempt from this tax.
I am working with ...
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Negative marginal utility and negative marginal product
In microeconomics, we usually 'allow' utility functions with negative partial derivatives, indicating a 'bad' commodity, such as $u(x,y)=x^2-y$. Naturally, a utility-maximising consumer with a usual ...
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Slope of isoquants
Consider a production function $f(L,K)=\sqrt{KL}$.
The |MRTS|=$K/L$, and $\frac{d|MRTS|}{dl}=\frac{-K}{L^2}$
However, if I use the expression given in Nicholson and Snyder (Microeconomic Theory, ...
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Intertemporal profit maximization
Assume a producer wishes to maximize the net present value, choosing optimal quantities of K and L. variables are time dependent. y is the production function, p is the price of y. K is capital, r is ...
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why are there heterogenous prices fixed for every unit of output
everyone says that it is because a monopoly decides the market's output, prices fixed per unit of the same keep decreasing.
question: if the firm has the ability to influence market prices, why would ...
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Global returns to scale
I have a production function of the form $f(x_1,x_2) = x_1^a x_2^b$ and I am trying to figure out what the global returns to scale would be given that $a,b \in (0,1)$.
This production function is ...
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How to derive the input demand functions from a perfect substitutes production function
I am struggling to derive the input demand functions from a production function with inputs that are perfect substitutes.
The production function is as follows:
$f(x_1,x_2) = (x_1+x_2)^\frac{1}{2}$
I ...
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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{...
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Price Elasticiyt of Demand & (AR - MR)
I have the following question:
Using this equation: $MR = P(1+\frac{1}{ε})$ and the attached graph. How does the vertical distance between the demand curve and MR curve at a given level of output ...
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Missing Non-Negativity Constraint?
We have the constrained maximisation problem:
A perfectly competitive firm produces one output with two inputs, capital $(k)$ and labour $(l)$. The rental cost of capital is equal to $r >0$ and ...
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Firms choosing upgrade & minimizing choice
Imagine hypothetically, there is a firm that has two option for production technology:
f(z) = √z but also the option to increase efficiency to g(z) = 2√z but this choice includes fixed cost F > 0.
...
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Derive cost function from production function
proportions production function as follows:
where the price of input is 1 and z2 is supposed to be a fixed factor of production. I've been having trouble finding the cost function because if z2 isn't ...
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Solve long run production function of a firm using technical rate of substitution
I don't understand the solution to a question which deals with the long run production function of a firm.
The question is:
Suppose a firm has a production function $f(x_1, x_1) = x_1^{0.5}x_2^{0.5}$, ...
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What is the difference between preferences of the producer vs the consumer?
The book I am working with (Rubinstein) states that in the case of the profit-maximizing producer, preferences are linear and the constraint is a convex set. Meanwhile, in the consumer model, ...
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Convexity of production sets and input requirement sets
The following question is from Microeconomic Analysis by Hal R Varian.
True or false? If V(y) is a convex set, then the associated production set Y must be convex.
The solution available says;
False. ...
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How are returns to scale of a non homogeneous production function defined?
Most of the production functions encountered in Intermediate Microeconomics are homogeneous (Cobb-Douglas, perfect substitutes, perfect complements).
So their returns to scale are easy to get, ...
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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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In Austrian economics, do producers have an ordering of preferences similar to consumers?
I watched a video from the Mises Institute where the lecturer mentioned that in Austrian economics, the consumer behavior that is observed is a result of their perception of the utility of the ...
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How to prove that the lower level set of a continuous function as a correspondence is continuous?
"If $s(•)$ is a continuous function, and $A(a):=\{x:s(x)\leq a\}$ is its lower contour set at $a$, then $A(•)$ is a continuous correspondence."
I can't find the right way to prove the upper ...
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How useful are basic economics (elasticity / consumer & producer theory) in real life?
I am thinking how these concepts will be applied in the industries / at a job.
For example I could see elasticity as useful in projecting the outcomes of supply ...
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Prove that if a production function is such that f'>0 and f''<0, then f'<Average Product
I was told in class that if we have a production function such that $f'(x)>0$ and $f''(x)<0$, then we have that the marginal product is less than the average product. That is $f'(x)<\frac{f(x)...
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Quasi fixed costs - two technologies
If a firm has the choice of using two production technologies to produce the same output:
A, featuring a quasi-fixed cost of 50 (i.e. 50 for all q > 0, 0 when q = 0), then a variable cost of 5q
B, ...
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Investigating the firm's supply function
Suppose the firm has a minimum cost function $C(\vec{w}, q)$ and sets up the following profit maximisation problem:
$max_{q} \text{ } pq - C(\vec{w}, q)$. The below FOC characterises the solution:
$p =...
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How do you calculate the contribution of each factor of production to the value of the final product?
How do I determine how much value that capital, labor, and land individually contributed to the value of a firm/good? Like what % of value came from capital vs labor vs land? I heard that this is ...
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Micro: proving that cost minimizing input vector for producing y cannot produce more than y
I am stuck at a very simple question. Let $V(y)$ be the set of all $x \in \mathbb{R}^n$ that can produce at least $y$. We are given that $V(y)$ is convex set.
Given $w$, factor prices, let
$$x^* = \...
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Does aggregate CRS imply firm-level CRS?
Suppose that a production set $Y \subset \mathbb R^I$ has the following two properties:
Constant returns to scale: $\forall y \in Y, \alpha \geq 0$, we have $\alpha y \in Y$.
Separability: For some $\...
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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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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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Interior Solution for profit maximisation problem
A function $c: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a cost function if
The value of function $c$ at $y = \textbf{0}$ is $0$: $c(\textbf{0}) = 0$
$c$ is continuous on the ...
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Walras Law in a production economy with fixed costs
Consider a price taking firm with fixed costs $fc \geq 0$:
\begin{align*}
\Pi
&=
\max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\}
\end{align*}
A representative household owns this firm:...
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Properties on conditional demand correspondence from the textbook of Mas-Colell et al
I have a question on the properties of conditional demand correspondence
Let $z(w,q)$ be the conditional factor demand correspondence, i.e. the solution of the cost minimization problem
\begin{align}
\...
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If production function is concave, then demonstrate that profit function will also be concave
Show that concavity of firm's production function implies concavity of its profit function.
(Hint: For a concave function, first order conditions gives the vector that maximizes the function)
...
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Why was activity analysis abanadoned as a field of research?
Activity analysis was a thriving research area in the 1940's and 1950's. It was fruitful enough to earn the Nobel prize for Tjalling Koopmans. But it seems to have been abandoned altogether. Mas ...
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The existence of solution for profit maximization problem
I'm thinking about the conditions for existence of solution of this profit maximization problem(PMP), i.e.,
$\max_{z \in R_+^{K-1}} pf(z) -wz$,
where $z \geq 0$: input vector, $p>0$: the price of ...
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Parameter value for a CES production function
Consider a firm with the following CES production function, which utilizes only two production factors (capital and labor) whose prices are, respectively, $r > 0$ and $w > 0$:
$$ y = \gamma \...
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Lerner Index Interpretation?
How do you interpret the Lerner Index?
I ask because at Uni. we have been told that, for monopoly, when the producer max. his profit, he sets the price such as the demand is elastic and the lerner ...
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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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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} ...
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Do property values capture producer choice in agriculture?
I am interested in conducting research into how climate change impacts the social welfare of a country, particularly how it affects producers of agricultural product. My immediate thought was that as ...
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Perfectly elastic supply
How would you algebraically write a perfectly elastic supply?
Will it be infinite at price = 4? (The choice of the number 4 is completely arbitrary)
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Value Function For Durable-Good Monopolist with General Distribution
It is known that with a unit mass of consumers, each of whom has a value distributed between 0 and 1, one can think of the monopolist solving
\begin{equation}
\max_{p} \ p[1-F(p)]
\end{equation}
when ...
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How can i determine the homogeneity degree of Stone Gaery function? [closed]
I dont know how to demonstrate homogeneity degree of this function
$(X-\alpha)^{\beta}(Y)^{1-\beta}$
Any idea?
Thanks.
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Intermediate Case of Bertrand and Cournot
I am wondering whether there is a model of oligopolies in which we have some intermediate case of Bertrand and Cournot competition. What I do not mean by "intermediate" is the mixed Bertrand - Cournot ...
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Finding long run equilibrium price, quantity and number of firms with a linear average cost function
I've been been brushing up on my micoreocnomics lately and I came across a question in Perloff that looked really simple, but for some reason I am struggling to answer:
Assume we are in the long run ...
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Changing Constant Factor Demands
I’ve been given this true false question: Consider the minimization of wL + rK given F(K, L) $\geq$ Q with F(K, L) strictly increasing in K and L. The conditional factor demands K*(Q, w, r) and L*(Q, ...
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How is Aggregate Supply(Willing) equal to National Income(Actual)?
Acc. to definition of Aggregate Supply
It is the total value of final goods and services that the producers are willing to supply in country .
Definition of National Income
It is the value of ...
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