Suppose there are 3 agents i ∈{1, 2, 3} with preferences over 3 objects j ∈{a, b, c} as follows: 1 : c b a 2 : b c a 3 : b a c Consider the random allocation given by the following probability shares: Agent Good a b c 1 0.5 0 0.5 2 0.25 0.5 0.25 3 0.25 0.5 0.25 Is this allocation ordinally efficient?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.5P
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Suppose there are 3 agents i ∈{1, 2, 3} with preferences over 3 objects j ∈{a, b, c} as follows: 1 : c b a 2 : b c a 3 : b a c Consider the random allocation given by the following probability shares: Agent Good a b c 1 0.5 0 0.5 2 0.25 0.5 0.25 3 0.25 0.5 0.25 Is this allocation ordinally efficient? Is it ex-ante weakly envy-free? Be sure to explain how you arrived at your answer.  

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