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3 votes
1 answer
190 views

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 ...
Nicolas Torres's user avatar
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 − ...
sachin's user avatar
  • 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 ...
Nicolas Torres's user avatar
5 votes
1 answer
2k views

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: $u_A = x_A + y_A$ $u_B = s x_A + y_A$ $...
Nicolas Torres's user avatar
1 vote
1 answer
209 views

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 ...
L1234's user avatar
  • 33
1 vote
1 answer
424 views

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 ...
KK econ's user avatar
  • 11
1 vote
1 answer
901 views

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 $w_B(1,\alpha)$ ...
studentp's user avatar
  • 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 ...
PGupta's user avatar
  • 217
4 votes
1 answer
303 views

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(...
clueless's user avatar
  • 1,579