20.There are two groups, each with a utility function given by where

M=144 is the initial wealth level for every individual. Each member of group 1 faces aloss of 44 with probability 0.5. Each member of group 2 faces the same loss withprobability 0.1.a.What is the most a member of each group would be willing to pay to insure againstthis loss?b.If it is impossible for outsiders to discover which individuals belong to which group,how large a share of the potential client pool can the members of group 1 be beforeit becomes impossible for a private company with a zero-profit constraint to provideinsurance for the members of group 2? (For simplicity, you may assume that insur-ance companies charge only enough in premiums to cover their expected benefit pay-ments and that people will always buy insurance when its price is equal to or belowtheir reservation price.) Explain.

*21.Given a choice between

A

(a sure win of 100) and

B

(an 80 percent chance to win 150and a 20 percent chance to win 0), Smith picks

A.

But when he is given a choice between

C

(a 50 percent chance to win 100 and a 50 percent chance to win 0) and

D

(a 40 per-cent chance to win 150 and a 60 percent chance to win 0), he picks

D.

Show thatSmith’s choices are inconsistent with expected utility maximization

a) What is the most a member of each group would be willing to pay to insure against this loss?

*20.There are two groups, each with a utility function given by where

M

144 is the initial wealth level for every individual. Each member of group 1 faces aloss of 44 with probability 0.5. Each member of group 2 faces the same loss withprobability 0.1.a.What is the most a member of each group would be willing to pay to insure againstthis loss?b.If it is impossible for outsiders to discover which individuals belong to which group,how large a share of the potential client pool can the members of group 1 be beforeit becomes impossible for a private company with a zero-profit constraint to provideinsurance for the members of group 2? (For simplicity, you may assume that insur-ance companies charge only enough in premiums to cover their expected benefit pay-ments and that people will always buy insurance when its price is equal to or belowtheir reservation price.) Explain.

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