Questions tagged [producer-theory]
Study of the behavior of firms in organizing their production and allocating productive resources.
65
questions
3
votes
2answers
73 views
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 ...
2
votes
2answers
79 views
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^* = \...
1
vote
0answers
38 views
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 $\...
12
votes
6answers
2k 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) ...
0
votes
0answers
41 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 ...
7
votes
1answer
102 views
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 ...
4
votes
1answer
86 views
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:...
5
votes
1answer
81 views
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}
\...
2
votes
1answer
148 views
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)
...
4
votes
1answer
251 views
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 ...
4
votes
2answers
212 views
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 ...
1
vote
0answers
34 views
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 \...
1
vote
0answers
22 views
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 ...
6
votes
1answer
605 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 ...
1
vote
0answers
114 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
38 views
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 ...
0
votes
1answer
49 views
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)
1
vote
1answer
54 views
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 ...
-2
votes
1answer
35 views
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.
5
votes
1answer
86 views
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 ...
2
votes
0answers
2k views
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 ...
-2
votes
1answer
139 views
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, ...
2
votes
0answers
307 views
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 ...
1
vote
0answers
17 views
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
...
2
votes
1answer
165 views
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 ...
1
vote
1answer
2k views
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 ...
4
votes
1answer
85 views
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 ...
0
votes
1answer
89 views
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, ...
2
votes
0answers
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 ...
0
votes
3answers
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.
0
votes
1answer
986 views
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 ...
2
votes
1answer
224 views
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 ...
1
vote
1answer
421 views
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 $0$...
3
votes
0answers
99 views
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 ...
3
votes
2answers
64 views
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 ...
1
vote
1answer
757 views
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{\...
1
vote
0answers
17 views
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 ...
1
vote
0answers
850 views
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 ...
1
vote
1answer
22 views
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,...
11
votes
4answers
2k views
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 ...
2
votes
2answers
111 views
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 ...
2
votes
1answer
43 views
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. ...
0
votes
2answers
2k views
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......
3
votes
2answers
1k views
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 ...
4
votes
1answer
302 views
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})\...
1
vote
2answers
2k views
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 ...
1
vote
0answers
318 views
Curvature of Cost and Production Function
I have been trying to understand the duality theory between cost and production function. Please let me know if my following statement is correct;
If the cost function $C(w,q)$ is convex in $q$, the ...
10
votes
3answers
2k views
CES Production Function with $\rho>1$
In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho} $, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the ...
1
vote
0answers
692 views
Monotonic Transformation
How does positive monotonic transformation of production function effect the resulting profit function?
For example if we had production function $f(x) $ and that gave profit function $\pi(p,w)$. Now ...
3
votes
1answer
117 views
Homothetic Production Technologies
Can someone suggest a good resource on homothetic technologies and what properties they imply about cost function, profit function, input demands, output supply etc? Also is it possible to have ...
