Suppose there are two types of people: Healthy and Unhealthy. It costs more to insure unhealthy people because they are likely to incur more medical bills. Suppose the marginal cost (MC) of providing an insurance policy is $1,000 for a healthy person and $4,000 for an unhealthy person. Assume healthy people are willing to pay $1,500 for health insurance, and unhealthy people are willing to pay $5,000. Suppose the insurance company charges P = MC so as to earn zero profit.

a) With complete information, will all people be insured? If no, explain why. If yes, what would be the price of insurance for each type of people?

b) Now suppose there is asymmetric information. People know whether they are healthy or unhealthy, but the insurance company can't tell. However, it knows that 20% of the population is unhealthy. If people can choose whether to buy insurance or not, who will buy insurance? And what will be the price of insurance in equilibrium? Is this outcome efficient? Explain why or why not.

c) Suppose government provides a medical service plan (MSP), which is a universal compulsory medical insurance that everyone has to buy. How should MSP set the price to just break even? Is the outcome efficient? Briefly explain.