nsurance Market. Consider the following simple model of health insurance. Let there be three types of people, LOW, MEDIUM, and HIGH risk, whose yearly medical expenses are $0 with 95% probability and $25K, $50K, and $100K (respectively) with 5% probability for the LOW, MEDIUM and HIGH groups. All three risk types are equally represented in the population, and all people have an initial wealth level of $100K, and a utility function over wealth of u(x) = x(where x is measured in thousands of dollars). To be clear, a HIGH risk person therefore has initial wealth of $100K and a 95% chance of $0 medical expenses, but a 5% chance of $100K in medical expenses. Insurers only offer the simplest policy, where people pay a premium but no deductible and medical expenditure is fully reimbursed. Assume that insurers have no costs other than the expected payouts to their policyholders. a) Compute the expected cost to the insurer for each type of customer. Also, compute the highest premium that each type of consumer is willing to pay (according to expected utility). b) If it were required that all people be insured, and insurance is competitive so that premiums equal average cost, what would the premium be? c) If insurance were optional, and again insurance is competitive so that premiums equal average cost, what premium would insurers charge? And which risk types would choose to buy insurance at that premium? (Hint: Note t