Consider a pure-exchange economy with four individuals i = 1,2,3,4 and two pri­v

Question

Consider a pure-exchange economy with four individuals i = 1,2,3,4 and two pri­vate goods X and Y. The utility functions are U1 = min{x1,y1}, U2 = {x2,y2,}, U3=x3 and U4 = x4 + y4 where xi denotes player is consumption of good X and yi denotes player i's consumption of good Y The total endowment of good X is 10 The total endowment of good Y is 20. Which of the following statements is (are) TRUE? In every Pareto efficient allocation, y4 >= 10 x1 = 1 ,y1 = 1. x2 = l,y2 = 1, x3 = 8, y3 = 0. x4 = 0, y4 = 18 is a Pareto efficient allocation. Only I. Only II. Both I and II. Neither I nor II.

Explanation / Answer

pereto wil be greater than 20/2 ie 10

..

calculating pereto optimal front we ger x1 =1 and y1=1 x2=1 y2=1 x3=8 y3=0 x4 =0 y4 =18

hennce answer is

c. both 1 and 2

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