# Tag Info

### Question for general equilibrium

To find efficient allocations in this economy, we can first determine the production possibility frontier (PPF) which is given by the line segment $\dfrac{x}{2}+y=100$ where $x\in[0,200]$. Pareto ...
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### Weird Leontief production function

This is not a weird case, but a Leontief production function which is not homogeneous of degree one, but homogeneous of degree $b$. You can see this if you use the connection between a C.E.S. ...
• 33.9k
Accepted

• 3,708

• 2,259
Accepted

### Pareto set with Cobb-Douglas and Leontief preferences

I believe you are correct. The points for which Ya = 0 and $$0\le Xa \le 4$$ will be all Pareto efficient points. Proof: Consider an allocation like (2,0). The ...

### Pareto set with Cobb-Douglas and Leontief preferences

The bottom right origin is actually not in the Pareto set. At that point, $(x_A,y_A)=(8,0)$, so $U_A(x_A,y_A)=0$. Similarly, $(x_B,y_B)=(0,4)$, so $U_B(x_B,y_B)=0$. As an example, $B$ could give ...

• 7,069
1 vote

### Walrasian demand with a twist of Leontief function

$u(x_1,x_2)=\min(x_1,x_2)+5\max(x_1,x_2)=\max(x_1+5x_2,5x_1+x_2)$ which is not quasi-concave, but is an increasing quasi-convex function. So, demand will be at one of the two end-points of the budget ...
• 9,216
1 vote

### Leontief input output model with column sum greater than 1

You are right when saying that mathematically in the cited theorem the condition of column sums being less than 1 is not an "if and only if" condition and thus exceptional circumstances are ...
1 vote
Accepted

### Leontief input output model with column sum greater than 1

In terms of if and only if statements according to Peterson & Olinick (1982); A substochastic matrix A is productive if and only if $I-A$ is nonsingular. In substochastic matrix the sum of ...
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1 vote

### Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$

We solve the problem $$\max U(x_1,x_2,x_3) = \min\{x_1,x_2\} + x_3$$ subject to $$x_1 p_1 + x_2 p_2 + x_3 p_3 = I$$ From the min term we ...
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