Exchange Economy question!Please refer to the attached pictures and please solve them with the numbers and graphs given!! Thank you so much! Problem 3 (Exchange Economy). Consider a pure exchange economy with two consumers and twogoods. Suppose that consumer i's utility function is u(x, y) = x/51/5.(1) Derive the equation that characterizes the Pareto efficient allocations when there are w units ofgood j are present in the economy. (2) Draw all Pareto efficient allocations in an Edgeworth box diagram below. For the rest ofquestions, assume that consumer i's initial endowments is w₁ = (4/5,1/2), and a₂ = (1/5,1/2),respectively. Indicate the allocations that are Pareto efficient AND Pareto improvement overthe initial allocation (@₁,w2). This task requires you to carefully draw two indifference curves;one for consumer 1 that represents the utility level of u(@₁), and the other for consumer 2 thatrepresents the utility level of u(@2).10.90.820.70.60.50.40.30.20.10origin forperson 100.10.20.30.40.5good 10.60.70.80.9origin forperson 2z pool

Pareto efficient allocation refers to that point deviating from which no consumer can be made better…

Problem 3 (Exchange Economy). Consider a pure exchange economy with two consumers and two goods. Suppose that consumer i's utility function is u(x, y) = x/5y1/5. (1) Derive the equation that characterizes the Pareto efficient allocations when there are w units of good j are present in the economy.

Problem 3 (Exchange Economy). Consider a pure exchange economy with two consumers and two goods. Suppose that consumer i's utility function is u(x, y) = x/5y1/5. (1) Derive the equation that characterizes the Pareto efficient allocations when there are w units of good j are present in the economy.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Exchange Economy question!

Please refer to the attached pictures and please solve them with the numbers and graphs given!! Thank you so much!

Problem 3 (Exchange Economy). Consider a pure exchange economy with two consumers and two
goods. Suppose that consumer i's utility function is u(x, y) = x/51/5.
(1) Derive the equation that characterizes the Pareto efficient allocations when there are w units of
good j are present in the economy.

(2) Draw all Pareto efficient allocations in an Edgeworth box diagram below. For the rest of
questions, assume that consumer i's initial endowments is w₁ = (4/5,1/2), and a₂ = (1/5,1/2),
respectively. Indicate the allocations that are Pareto efficient AND Pareto improvement over
the initial allocation (@₁,w2). This task requires you to carefully draw two indifference curves;
one for consumer 1 that represents the utility level of u(@₁), and the other for consumer 2 that
represents the utility level of u(@2).
1
0.9
0.8
2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
origin for
person 1
0
0.1
0.2
0.3
0.4
0.5
good 1
0.6
0.7
0.8
0.9
origin for
person 2
z pool

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