# Questions tagged [leontief]

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### How to solve a Leontief Production function?

I am solving for the Leontief production function in the form of y= min {L^1/2 , K^1/2} , in the short run (fixed K) and in the long run respectively. I am asked to solve the production in terms of w, ...
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1 vote
844 views

### How to find the contract curve for a funky utility involving the min operator?

Suppose a pure exchange economy where agents’ ($A$ and $B$) preferences are given by the following utility functions: $u_A = \min(3x+y,x+3y)$ $u_B = x^\frac{1}{2} y^\frac{1}{2}$ Find the contract ...
• 2,249
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### Interpretation of the Elements of the Leontief Inverse (Total Requirements Matrix)

I found what I believe to be slightly different interetations of the individual elements of the Leontief Inverse (total requirements matrix): Miller and Blair (2009) just after Equation (2.12) mention ...
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1 vote
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### 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 ...
• 113
1 vote
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### 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
76 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
5k 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 ...
• 33
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### 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 \...
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### Leontief preferences and 2nd welfare theorem

Does the 2nd welfare theorem hold with Leontief preferences? If not, which of the assumptions does not hold?
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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 ...