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

Question

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)?