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Tagged with edgeworth-box pareto-efficiency
9 questions
3
votes
1
answer
190
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Find the Pareto Efficient allocations and Competitive Equilibrium when both agents have funky functions
I'm trying to solve this General Equilibrium excercise which I find quite challenging as both agents have funky utility functions.
Find the Pareto Efficient allocations and Competitive Equilibra for ...
- 2,351
2
votes
1
answer
220
views
Find the set of Pareto efficient allocations. $U_1 = -|x_1-2|$ and $U_2 = −|x_2 − 8|$
A professor has 20 hours to allocate between two PhD students. Let x1 and x2 be the time allocated to the two students. The utility of each student is as follows:
$U_1 = −|x_1 − 2|$ and $U_2 = −|x_2 − ...
- 23
1
vote
1
answer
1k
views
How to find the contract curve for a funky utility involving the min operator?
Suppose a pure exchange economy where agents’ ($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 ...
- 2,351
5
votes
1
answer
2k
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How to find the contract curve when both agents have linear utilities?
I'm trying to solve the following excercise:
Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = s x_A + y_A$
$...
- 2,351
1
vote
1
answer
208
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Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)
The one version of the Second Welfare Theorem states that: if there exists a competitive/Walrasian equilibrium and an endowment $X$ is Pareto efficient, then there is a price vector $\hat{P}$ for ...
- 33
1
vote
1
answer
424
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Edgeworth Box (Non-Convex preference)
Consider a situation that agent A's indifference curves are concave, while B’s indifference curves are convex and both sets of indifference curves have exactly the same shape. A northeast movement ...
- 11
1
vote
1
answer
900
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Find the set of Pareto efficient allocations
There is an exchange economy with two people and two goods.
Utility functions are
$u_A(x_A, y_A)=\max\{x_A, y_A\}$
$u_B(x_B, y_B)=\max\{x_B, y_B\}$
Endowments are $w_A(1,\alpha)$ and $w_B(1,\alpha)$ ...
- 192
1
vote
1
answer
194
views
Pareto Set with strictly convex preferences
Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A $ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10).
The contract curve's equation turns out ...
- 217
4
votes
1
answer
303
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Contract curve and Pareto frontier
Consider an exchange economy with two agents.
Each agent $i \in \{1,2\}$ derives utility $u^i(x_1,x_2) \in \mathbb R$ by consuming $(x_1,x_2) \in \mathbb R_+^2$.
Let $u_j^i(x_1,x_2) = \partial u^i(...
- 1,579