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? 

(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)?