All Questions
Tagged with optimization production-function
16 questions
2
votes
1
answer
58
views
Return to scale of a production function, $q = L^\lambda + K^\gamma$, is determining it possible in that general form?
Given the production function $q = L^\lambda + K^\gamma$, how do we determine the return to scale for different value of $\lambda$ and $\gamma$?
I know we have to determine the homogeneous degree of ...
- 41
1
vote
2
answers
42
views
How to determine if a production function in a functional form has diminishing marginal rate of technical substitution?
For production function $q(L,K) = L^\lambda + K^\gamma$ The MRST is defined as
$\frac{\lambda L^{\lambda-1}}{\gamma K^{\gamma-1}}$. Is it correct and sufficient to say that in order for MRTS to be ...
- 41
1
vote
0
answers
33
views
question about production optimization
the question is,
if Q = AK^a(HL)^b
and the parameters are:
(A =100) (K = 10000$) (H = 1) (L = 100 person) (a = 0.5) (b = 0.5)
P = 5 per unit, R = interest rate of 3 percent per year , W = 3 per ...
- 11
2
votes
0
answers
99
views
Leontief function nested in a cobb-douglas function for a computable general equilibrium
I am currently trying to build a CGE model, and I'm stuck with the specification of the agriculture sector. I'm trying to understand how to do nested production functions and also how to solve them. I ...
- 31
1
vote
0
answers
21
views
Technology Parameter In Converted Minimisation Problem
Question:
I want to understand what's going on with respect to the technology parameter $A$ when i convert this minimisation problem into a maximisation problem. The issue is only revealed when i use ...
- 1,011
2
votes
1
answer
369
views
Arguments for Concavity or Quasi-concavity
I'm faced with questions that want me to show that a utility or production function is either concave, or if not then quasi-concave so that we can apply the KKT conditions.
For example the production ...
- 1,011
2
votes
1
answer
337
views
CRS, Homothetic Functions, and constant MRTS
Questions
When our Isoquant map exhibits constant MRTS along a ray from the origin making. Why do we make specific reference to.
Constant returns to scale
Homothetic Functions
I'm asking because it ...
- 1,011
1
vote
1
answer
178
views
Mixed Partial Derivatives in Profit Function
$\pi(x,z) = p(a\ln(x) + b\ln(z)) - w_xx - w_zz$
Question 1:
Using the first order conditions, we get:
$x = \frac{pa}{w_x}$
$z = \frac{pb}{w_z}$
What do we call these Input demand functions as a ...
- 1,011
0
votes
1
answer
43
views
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 ...
- 61
2
votes
0
answers
217
views
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 $P_3/P_4<1/2$
...
- 192
1
vote
1
answer
62
views
Deriving factor allocation of production function
I am trying to solve an allocation problem for a nested CES production function with three factors.
The production function we posit is:
$$
F(K, \mathbf L, \mathbf C) = [\alpha K^\rho + \sum_{i\not\in ...
- 111
4
votes
1
answer
362
views
Does global maximum of CRS Cobb-Douglas profit exist
In most macroeconomic papers it is taken as given that the aggregate prodution function is $Y=AK^{\alpha}L^{1-\alpha}$, and that the optimality conditions for inputs determine input demands:
$$
\max_{...
- 69
1
vote
0
answers
1k
views
Optimization problem of a Cobb-Douglas function with 3 inputs
A perfectly competitive firm uses 3 inputs to manufacture a certain product according to the following Cobb-Douglas production function:
$$
Q = A L_1^{\alpha_1} L_2^{\alpha_2} L_3^{\alpha_3}
$$
...
- 111
1
vote
0
answers
282
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
1
answer
358
views
General Equilibrium with Linear Production
I don't think I understand how optimization problems with a linear function work as of now. If you have a production economy with two agents, two goods and Cobb-Douglas utility representation, and you ...
- 53
5
votes
2
answers
4k
views
Transformation Function
In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (...
- 195