2. In a country, health insurance is provided by one non-profit making health insurance company. The insurance company charges the same premium to all and pays out full costs (i.e. the policyholder pays share of the medical costs). Half of the population is healthy and the other half is unhealthy. If an insured healthy person becomes ill, the full cost to their health insurance company is 1000. If an insured unhealthy person gets sick, the full cost is 10000 (as they will need more medical care). Suppose that in any year, the chances of any individual getting sick is 40% (regardless of how healthy they are generally). People know whether they are healthy but the insurance company does not.

(a) If everyone purchases insurance, what is the insurance premium?

(b) If only unhealthy people purchase insurance, what is the insurance premium?

(c) If each individual has the option of buying insurance, explain why adverse selection might be expected unless healthy people are highly risk averse.