Questions tagged [leontief]
The leontief tag has no usage guidance.
0
votes
1answer
36 views
Optimal choice for a weird leontief function
Compute the optimal choice for a consumer with the following utility function:
$$u(x_1, x_2) =\max \{\min(2x_1, x_2), \min(x_1, 2x_2)\}$$
I'm familiar with computing optimal choice for perfect ...
0
votes
1answer
48 views
Pareto set with Cobb-Douglas and Leontief preferences
If $U_A(x_A,y_A)=x_Ay_A$ and $U_B(x_B,y_B)=min(x_B,y_B)$ and the total endowments are (8,4), is the Pareto set given by the line joining the kinks of B (black line shown in the diagram)? Shouldn't the ...
2
votes
1answer
114 views
Marshallian demand with Leontif preferences
Consider a utility function on the form $u(q_{1},q_{2},q_{3}) = min\{\alpha ln(q_{1}) + (1 - \alpha) ln(q_{2}), ln(q_{3})\}$
I know that optimal behaviour requires $\alpha ln (q_{1}) + (1 - \alpha) ...
-1
votes
1answer
108 views
Expenditure minimization with Leontief utility
I need to solve the expenditure minimization in a context where $u(x,y) = min\{x,y\}$, i.e. where utility is Leontief.
The minimization problem is
$$\text{min}_{x,y}\,\,p_xx+p_yy \\
\text{subject}\,...
3
votes
2answers
102 views
What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept)
I encountered that nobody, even my profs and lecturers so far, has an intuitive way to explain what the Leontief inverse represents. Does somebody here?
As most people here would know, it goes:
$\ ...
6
votes
1answer
73 views
Leontief's Paradox and the amount of capital
Leontief (1953) showed that US exports in 1947 embodied considerably less capital and somewhat more labor than would be required for domestic production of competitive imports. \$2.55 million worth of ...
1
vote
0answers
125 views
Endowment increases but utility reduces
In an Edgeworth economy with two agents and two goods, Player A has endowment $\left(a,\,0\right)$ and utility $u_{A}\left(x_{1},\,x_{2}\right)=\min\left(\gamma x_{1},\,x_{2}\right)$ in which $\gamma&...
1
vote
1answer
431 views
Derivation long run cost function of three inputs with Leontief-like characteristics
Suppose that a firm produces a good using capital, skilled labor, and unskilled labor. Let $K$ denote the amount of capital,$L_1$ unskilled labor, $L_2$ skilled labor. The production function is $f(...
3
votes
1answer
2k views
Leontief function marginal product of labor/capital
Find marginal product of labor of a Leontief production function. For example,
$$f(L, K) = min\{\frac{L}{a}, \frac{K}{b}\}$$
MY ATTEMPT
Now as I understand it the marginal product of labor, $MP_L$ ...
1
vote
0answers
18 views
Perfect complement outputs with each output being composed of substitutable inputs
How does one solve the following maximization problem?
$\underset{K_1, K_2, L_1, L_2}{\text{maximize }} min\{K_1 + L_1,K_2 + L_2\}$
subject to $c(K_1 + \mu K_2) + \beta c(L_1 + \mu L_2)$
where $c(...
0
votes
1answer
30 views
why not use $Ap - p$ instead of $p - Ap$?
I am watching this video about the Leontief input-output model: https://youtu.be/hlaBURtSDO8?t=12m26s
One thing I don't understand is: why not use $Ap - p$ instead of $p - Ap$? It seems to make ...
1
vote
4answers
879 views
Weird Leontief production function
I am solving some micro related exercises and I came across this weird Leontief production function: $$Q =\left(\min\{K, L\} \right)^b$$
I am not sure how to solve it. I have to find the inputs' ...
1
vote
0answers
44 views
First Reference Leontief/Perfect Complements
I googled a lot and I'm still to find:
1. In which paper/book/reference do Leontief [production] functions make their first appearance?
Similarly
2. In which paper/book/reference do perfect ...
1
vote
1answer
2k views
maximizing leontief-type utility function
How do I maximize the utility function:
$ U(x,y)= max(ax,ay)+min(x,y) $ , where $ 0<a<1 $ with respect to prices $ p_{x}, p_{y} $ respectively and income $ m $.
I know leontief-type utility ...
7
votes
2answers
624 views
Constant Elasticity of Substitution: Special Cases
Take an $n$-commodity constant elasticity of substitution utility function,
$$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$
How do we show the following:
Show that as $\rho \...
3
votes
1answer
290 views
Leontief preferences and 2nd welfare theorem
Does the 2nd welfare theorem hold with Leontief preferences? If not, which of the assumptions does not hold?
8
votes
1answer
5k views
Leontief preferences
I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
20
votes
2answers
23k views
How can I obtain Leontief and Cobb-Douglas production function from CES function?
In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function,
$$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$
(where the ...
