Questions tagged [producer-theory]
Study of the behavior of firms in organizing their production and allocating productive resources.
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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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1
answer
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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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1
answer
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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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answer
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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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1
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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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Is the definition of Investment variable in Economics?
I studied that Investment is the expenditure incurred on the procurement of such goods that would help us in production of goods and services.
And mainly consists of Fixed and Inventory Investment
...
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Why does a homothetic function have constant ratio of marginal products along rays?
A homothetic ordering is defined as
$x \succeq y \Rightarrow \lambda x \succeq \lambda y \qquad \forall \lambda >0$
where $x,y \in \mathbb{R}^n$
Then, any differentiable function representing ...
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MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market
Suppose the Total Cost function of a firm in Perfect Competition is
given by: $$C(q) = 450 + 15q + 2q^2$$
The market price is $P = 15$ per unit
Determine the optimal quantity produced by ...
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How to improve the underperforming construction productivity by correcting its market failures?
Globally, labor-productivity growth in construction has averaged only 1 percent a year over the past two decades, compared with growth of 2.8 percent for the total world economy and 3.6 percent in the ...
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Consider the following production function $Q=min \left(\frac{L}{2a}, \frac{K}{4b}\right)$. Let $w$ and $r$ be the wage and rental rate respectively [closed]
The cost function associated with this production function is
$A) 2awQ\\
B) 4brQ\\
C) (wa + 2br)Q\\
D) None\; of\; the\; above$
What I have tried is:
We have the cost function $wL+rK=C$.
Since, here, ...
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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 ...
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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.
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Are all points on the Long Run Average Cost (LRAC) curve productively efficient?
The definition of productive efficiency is that any given output is produced for the lowest possible cost.
In the short run, only the minimum point on the SRAC curve is productively efficient - this ...
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Help with this microeconomics exercise
The question:
A price-taking farmer produces a crop with labor L as the only input.
His production function is:$$F(L) = 10L^{1/2} − 2L$$
He has 4 units of labor
in his family and he cannot hire ...
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Some doubts about netput vectors
I have started studying producer theory on my own and there are some confusions.
We know that a production plan is $y=(y_{1},y_{2},y_{3}....y_{L})$ where $ y_{i} $ is an output if its greater than $0$...
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Is it possible to derive the marginal product of an input using a transformation function?
I'm using a transformation function $F(\cdot)$ to describe a production set $y = (x, z, L, K)$, where $x$ and $z$ are private goods denoted by positive numbers, $L$ is labour input, $K$ is capital ...
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Pricing Education
On what basis do colleges/private schools price a given course assuming class size and direct costs are the same?
My current understanding is in my question on private school behaviour regarding the ...
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What is the meaning of the weights in a CES-production function?
In different paper I offen encounter two types of CES production functions
$y=\left[\left(1-\omega \right) x_{1}^{\frac{\sigma -1}{\sigma}}+ \omega x_{2}^{\frac{\sigma -1}{\sigma}} \right]^{\frac{\...
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Delaying wages in response to slack?
I'm reading a book about the economic development of South Korea during the 'miracle' period.
One of the points the author makes is the following:
A major source of industrial disputes was ...
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Shape of Isoprofit Curves for Strategic Complements
Two goods are strategic complements if:
$$\frac{\partial \pi_1}{\partial q_2}>0\;\text{and}\;\frac{\partial \pi_2}{\partial q_1}>0$$
The image below is a picture of best response functions and ...
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Retailer Price Setting for Existing Inventory in the Event of an Increase in Price Paid for the Good
If you are a retailer, and the price you pay for one of your retail goods goes up, how do you price the inventory you already had (which you paid a lower price for)?
Here is an example of a TFD (True,...
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Are There Giffen Inputs?
I am studying for my candidacy exams and I came across this question on a previous exam. The question is in the TFD (True, False, Debatable) section of the exam. The claim is:
There are no Giffen ...
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What would make a restaurant offer all-day breakfast?
Some restaurants particularly fast food ones offer breakfast food only during, well, breakfast hours. Other restaurants however offer breakfast food throughout their opening hours. Some restaurants ...
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Producer's cost for buying full solution vs. buying parts
This may be a very basic question.
From a producer's standpoint, what are the theoretical or empirical results on the comparison of cost between buying assembled or full solutions from suppliers vs. ...
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Does the contract curve always have to connect the initial points on an edgeworth box? Why or why not?
What if the contract curve goes out of bounds? In that case, do I assume it superimposes itself on the axes it is closest to?
I hope this was clear. Not sure how to explain this other than visually......
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Why are some goods without close substitutes not sold in some countries?
Especially in consumer electronics, a large number of goods are offered only in some countries. Usually this holds only for products which have some close substitutes available (e.g., screens, where a ...
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Elasticity of substitution in Jehle and Reny Advanced Micro (3rd ed) exercise 3.8
Letting $f_i(\mathbf{x})=\partial f(\mathbf{x})/\partial x_i$, ($\mathbf{x}$ is a vector, a commodity bundle, and $x_i$ is a scalar, commodity $i$ in the bundle) show that,
$\sigma_{ij}(\mathbf{x})\...
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Economic Order Quantity w/ no set up costs
Is it possible to modify the EOQ model to work in a purchasing environment when ordering costs are effectively $0$?
The classic EOQ model is:
$$
Q=\sqrt{2aK/h}
$$
with $a$ being demand, $K$ ordering ...
