Consider a competitive market for health insurance with 10000 potential costumers, which are divided into two groups. Assume that the number of people in group 1 (and, respectively, 2) is 9400 (and, respectively, 600). The probability of illness in group 1 is p1 = 0.01, whereas in group 2 it is p2 = 0.05. To treat an illness in either group costs 100000. All customers are risk averse, and the willingness to pay for insurance is 1200 in group 1, and 6000 in group 2.

(a) Describe the equilibrium assuming that the health insurance companies cannot differentiate between group 1 and group 2. Is the outcome efficient?

(b) Describe the equilibrium if the health insurance companies devise a test to distinguish between consumers of group 1 and 2. What can you say about efficiency? (c) What happens if the government forbids the insurance companies to discriminate between individuals from the two groups? Consider introducing a subsidy to assist individuals of group 2; and show it is increasing in both, the total population and the expected cost of treatment.