Posted by **John** on Wednesday, January 11, 2012 at 4:18pm.

There are two groups of individuals of equal size, each with a utility

function given by U(M) = sq. root(M), where M = 100 is the initial wealth

level for every individual. Each member of group 1 faces a loss of 36

with probability 0.5. Each member of group 2 faces the same loss with

probability 0.1.

(a) What is the maximum amount of money a member of each group

would be willing to pay to insure against this loss?

(b) Assume that it is impossible to discover which individuals belong

to which group. Will members of group 2 insure against this loss in

a competitive insurance market, where insurance companies o¤er

the same contract to everybody? Explain your answer.

(c) If insurance companies anticipate the result of part (b), what type

of contract will they o¤er in a competitive insurance market?

(d) Now suppose that the insurance companies have an imperfect test

for identifying which individual belongs to which group. If the test

says that a person belongs to a particular group, the probability

that he/she really does belong to that group is p < 1. How large

must p be in order to alter your answer to part (b)?

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