There are two groups of equal size, each with a utility function given by U(M) = √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 most a member of each group would be willing to pay to insure against this loss? b. In part (a), if it is impossible for outsiders to discover which individuals belong to which group, will it be practical for members of group 2 to insure against this loss in a competitive insurance market? (For simplicity, you may assume that insurance companies charge only enough in premiums to cover their expected benefit payments.) Explain.
c. Now suppose that the insurance companies in part (b) have an imperfect test for identifying which individuals belong to which group. If the test says that a person belongs to a particular group, the probability that he really does belong to that group is x < 1.0. How large must x be in order to alter your answer to part (b)?