Question

Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U =sqrt(C), where C is the amount of consumption that people have in any period. So long as they are healthy, individuals will consume their entire income of $16,000. If they need medical attention (and have no insurance), they will have to spend $12,000 to get healthy again, leaving them with only $4,000 to consume. Smokers have a 10% chance of requiring major medical attention, while nonsmokers have a 2% chance.

Insurance companies in Chimnesia can sell two types of policy. The "low deductible" (L-) policy covers all medical costs above $2,000, while the "high deductible" (H- policy only covers medical costs above $10,000.

(a) What is the actuarially fair premium for each type of policy and for each group?

(b) If insurance companies can tell who is a smoker and who is a nonsmoker and charges the actuarially fair premiums for each policy and group, show that both groups will purchase the L-policy

Suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company does not.

(c) explain why it is impossible at any price, for both groups to practice L- policies in this setting. Which groups if any, do you expect to buy L- policies, and at what price?

(d) Show that it is possible for both groups to purchase insurance, with one group buying L-policies and one group buying H-policies.

Answer 1