15. Chimnesia has two equal -sized groups of people: smokers and nonsmokers. Both types of people have
Question:
15. Chimnesia has two equal -sized groups of people:
smokers and nonsmokers. Both types of people have utility U ln(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 $15,000. If they need medical attention (and have no insurance), they will have to spend $10,000 to get healthy again, leaving them with only $5,000 to consume. Smokers have a 12% chance of requiring major medical attention, while non smokers have a 2% chance.
Insurance companies in Chimnesia can sell two types of policies. The “low deductible” (L-)
policy covers all medical costs above $3,000, while the “high deductible” (H-) policy only covers medical costs above $8,000.
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 non smoker and charge 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 purchase 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 group to purchase insurance, with one group buying L-policies and one group buying H-policies.
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