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### 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 ...
• 12.3k
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 ...
• 3,697

### 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, ...
• 8,466
Accepted

### How do I find the set of pareto optimal allocations?

In the economy you provided, set of feasible allocations is $\mathcal{F}=\{((x_1,y_1),(x_2,y_2))\in\mathbb{R}^2_+\times\mathbb{R}^2_+|x_1+x_2=2 \ \wedge \ y_1+y_2=1\}$ and is represented by points in ...
• 8,466

### Core in a replicated economy

In the economy provided in the question, competitive equilibrium allocations is equal to the set of efficient allocations. This along with the fact that the competitive equilibrium allocations always ...
• 8,466
Accepted

### Finding Pareto optimal allocations and Walrasian equilibrium allocations in the case of 3 goods

Pareto Optimality: Since preferences are convex in your case, you can find Pareto optimality in the same way. You need to solve $\text{MRS}^{A}_{v,w} = \text{MRS}^{B}_{v,w} = \text{MRS}^{C}_{v,w}$ ...
• 56

### Does the contract curve always have to connect the initial points on an edgeworth box? Why or why not?

The contract curve is the locus of Pareto optimal points in an Edgeworth box. What we get from that: To be P.O., an allocation must be feasible. So, the contract curve does not extend beyond the ...
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### Fair and efficient allocation of "family goods"

Suppose there are two families: Family U has $n_u$ members, and family V has $n_v$ members. Utility function of member $i$ of family U is: \begin{eqnarray*} u_i(x_u, y_u) = a_ix_u + y_u \end{eqnarray*}...
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### Net and gross market clearing in endowment economy

The issue here is that market clearing can be defined in gross as well as in net terms. Gross vs. net Suppose I need 10 eggs for the next two weeks, and I don't intend to have any left over (I am ...
• 29.5k
Accepted

### How to find the competitive equilibrium?

Here is a lazy tricks-based approach that requires almost no calculations: First, we know that every equilibrium allocation must be Pareto efficient by the first welfare theorem. If $B$ consumes ...
• 12.3k

### Finding Pareto optimal allocations and Walrasian equilibrium allocations in the case of 3 goods

To add to my previous answer (and to reply to your comment), the set of equations for Pareto optimality include the MRS equations and the feasibility equations. MRS equations: \begin{align} \text{MRS}^...
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Accepted

• 8,466
1 vote

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1 vote

### Fair and efficient allocation of "family goods"

Suppose the preferences of all agents in all families are monotone and convex (the standard assumptions of consumer theory). Then, a Pareto-efficient envy-free allocation always exists when there ...
• 3,065

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