The cost of a hospital visit is $20,000. In a given year, a healthy person has a 10% chance of needing a hospital visit and an unhealthy person has a 20% chance. Half the population is healthy and half is unhealthy.

(a) By law, everyone is required to purchase hospital insurance. There is a monopoly provider of insurance who is required by law to charge the (actuarially) fair price for the insurance. This insurance company knows the information above but does not know which people are healthy and which people are unhealthy. What price will be charged for insurance? Is there adverse selection in this market? Explain briefly.

(b) The government repeals the law requiring everyone to buy insurance but still requires the insurance company to charge the (actuarially) fair price for the people who buy insurance. Healthy people and unhealthy people are risk-averse and have a risk premium of $500. The company still does not know who is healthy or unhealthy. In equilibrium, what will be the price of insurance, and who will buy it? Does the market exhibit adverse selection? Explain briefly.

(c) Suppose the share of healthy people in the market is x, and the share of unhealthy people is (1 - x). For what values of x is adverse selection a problem, assuming nothing else changes from the question in part (b) above? (Provide bounds on x using inequality signs.)