Skip to main content
7 votes
Accepted

Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Yes. The Debreu version of the Sonnenschein-Mantel-Debreu theorem guarantees that excess demand has to satisfy very little restrictions if there are as many consumers as commodities. An explicit ...
Michael Greinecker's user avatar
5 votes
Accepted

How to find the contract curve when both agents have linear utilities?

I rewrite the problem of maximization you wrote (I omit the endowments): $\max x_A + y_A \;\;\qquad (1)$ subject to $s x_B + y_B = \overline{U}\qquad (2)$. This problem can be seen as a problem of ...
BakerStreet's user avatar
  • 3,697
5 votes

Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Here is another example with two consumers (A and B), two goods (X and Y): \begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, ...
Amit's user avatar
  • 8,476
4 votes
Accepted

CES utility function in an Edgeworth box

There seems to be some confusion in the expression for $x^*_i$ in the question that whether $i$ is for consumer of for the good. Assuming $i$ is for consumer: Let $x^*_i = (x_1^i,x_2^i)'$ be the ...
Dayne's user avatar
  • 1,725
3 votes
Accepted

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

Given a pure-exchange economy: $u_1(x_1,y_1) = \min(3x_1+y_1,x_1+3y_1)$, $u_2(x_2,y_2)= x_2^{0.5}y_2^{0.5}$ Total Endowments of X and Y are $\omega^X > 0$, and $\omega^Y > 0$, respectively. ...
Amit's user avatar
  • 8,476
3 votes
Accepted

Shape of contract curve in an Edgeworth-Box economy

The answer is no both to the if and to the only if parts. If counterexample: For $u_{1,2} = \ln x + y$ and aggregate quantities (4,4) it is easy to check that the allocation (1,1),(3,3) is not Pareto-...
Giskard's user avatar
  • 29.5k
3 votes

In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?

Assuming that the total endowment of labor and capital is both equal to $1$, consider these examples with CRS technologies and efficient points on both sides of the diagonal of the box: Example 1: $x =...
Amit's user avatar
  • 8,476
2 votes
Accepted

Offer curves in general equilibrium

In the picture below offer curve of individual 1 is given by lines connecting $E$ to $O_1$ and $O_1$ to $O_2$. And offer curve of individual 2 is given by lines connecting $E$ to $O_2$ and $O_2$ to $A$...
Amit's user avatar
  • 8,476
2 votes

Edgeworth Box (Non-Convex preference)

If total endowments are $(\bar x,\bar y)$ and $A$ has utility function $u_A(x_A,y_A)$, then $B$'s utility function $u_B(x_B,y_B)\equiv -u_A(\bar x-x_B,\bar y-y_B)$ has the same indifference curves as $...
VARulle's user avatar
  • 6,825
2 votes
Accepted

Find the set of Pareto efficient allocations

We'll consider three cases: For $\alpha \in [\frac{1}{2}, 2]$, there are only two Pareto efficient allocations: $\big\{\big((2,0),(0,2\alpha)\big), \big((0,2\alpha),(2,0)\big) \big\}$ For $\alpha >...
Amit's user avatar
  • 8,476
2 votes

Shape of contract curve in an Edgeworth-Box economy

This answer assumes you understand the defining property of homothetic functions, namely, slope of their level curves being equal for a given input ratio. First let's understand what is the diagonal; ...
Shaikh Ammar's user avatar
2 votes
Accepted

How to find the Walrasian equilibrium for non monotonic utility functions?

Set of Pareto efficient allocations (or contract curve) is the set of all feasible allocations satisfying $1 \leq x_1=y_1\leq 3$. This is the line segment connecting points A and B in your graph. Also,...
Amit's user avatar
  • 8,476
2 votes

Finding Walrasian equilibria when Walrasian demands are not unique

let us first write the demand functions of individual $A$ and $B$ $$(x_A^d,y_A^d)(p_x,p_y,m_A)\in\left\{\begin{matrix} (\frac{m_A}{p_x},0) & ,\frac{p_x}{p_y}<1\\ (0,\frac{m_A}{p_y}) & , \...
mynameparv's user avatar
2 votes
Accepted

Find the set of Pareto efficient allocations. $U_1 = -|x_1-2|$ and $U_2 = −|x_2 − 8|$

To answer your question, you can't use the Edgeworth box in this kind of setup because it is used for an economy where we have two goods and two agents. However, there exists an alternative graphical ...
mynameparv's user avatar
1 vote
Accepted

Edgeworth Box for exchange economy

Not quite. The line you have drawn turns out to be the contract curve, but from this figure it's not clear how you get this line, because the indifference curves for the two utility functions are ...
VARulle's user avatar
  • 6,825
1 vote
Accepted

Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)

In every competitive equilibrium, a consumer's endowment is in their budget set. Since they choose an optimal point in the budget set, every consumer in a competitive equilibrium will receive a bundle ...
Michael Greinecker's user avatar
1 vote

In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?

I have understood why constant returns to scale imply efficiency locus lying on one side of the diagonal, but not why this does not imply that there are no factor intensity reversals taking place. My ...
Shaikh Ammar's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible