Suppose that half the population is healthy and the other half is unhealthy. If an insured healthy person gets sick, the full cost to the insurance company is $ 1,000. If an insured unhealthy person gets sick, the cost to the insurance company is $ 10,000. In a given year, any one person (healthy or unhealthy) has a 40% chance of getting sick. People know whether they are healthy but the insurance company does not. The insurance company offers complete, actuarially fair insurance at the same price to everyone. The insurance company covers all medical expenses of its policyholders, and its expected profit is zero.
a. If everyone purchases insurance, what is the price of the insurance?
b. If only unhealthy people purchase insurance, what is the price of the insurance?
c. If each person has the option of buying insurance, explain why adverse selection might be expected unless healthy people are highly risk averse.