Answer the questions based on the model given in the image:a. What is the set of Pareto optimal outcomes in this economy? Justify your answer.b. What is the competitive equilibrium in this economy assuming price of good 1 is set to 1. Specify whether the competitive equilibrium is pareto optimal.c. Now consider another economy where everything is as before, apart from individual 2’s preferences, which are as follows: among any two any bundles consisting of X and Y, individual 2 prefers the bundle which has a larger amount of commodity X irrespectiveof the amount of commodity Y in the two bundles, andbetween any two bundles with the same amount of X, she prefers the one with a larger amount of Y. (not sure but these are perhaps lexicographic preferences)Find the set of Pareto optimal outcomes in this economy. 1. Consider an exchange economy consisting of two individuals 1 and 2, and two goods,X and Y. The utility function of individual 1 is U1 = X1 + Y1, and that of individual 2 ismin{X2, Y2}, where X; (resp. Y;) is the amount of X (resp. Y) consumed by individual i,where i = 1,2. Individual 1 has 4 units of X and 8 units of Y, and individual 2 has 6 unitsof X and 4 units of Y to begin with.

Given: For individual 1: U1 = X1 + Y1 For individual 2: U2 = min{ X2 , Y2 } X1 = 4 units Y1 = 8…

Answered: Answer the questions based on the model…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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Answer the questions based on the model given in the image:

a. What is the set of Pareto optimal outcomes in this economy? Justify your answer.

b. What is the competitive equilibrium in this economy assuming price of good 1 is set to 1. Specify whether the competitive equilibrium is pareto optimal.

c. Now consider another economy where everything is as before, apart from individual 2’s preferences, which are as follows:

among any two any bundles consisting of X and Y, individual 2 prefers the bundle which has a larger amount of commodity X irrespective
of the amount of commodity Y in the two bundles, and
between any two bundles with the same amount of X, she prefers the one with a larger amount of Y. (not sure but these are perhaps lexicographic preferences)

Find the set of Pareto optimal outcomes in this economy.

1. Consider an exchange economy consisting of two individuals 1 and 2, and two goods,
X and Y. The utility function of individual 1 is U1 = X1 + Y1, and that of individual 2 is
min{X2, Y2}, where X; (resp. Y;) is the amount of X (resp. Y) consumed by individual i,
where i = 1,2. Individual 1 has 4 units of X and 8 units of Y, and individual 2 has 6 units
of X and 4 units of Y to begin with.

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