Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U=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 "zero-deductible" (L)policy covers all medical costs, while the "high-deductible" (H)policy covers only 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, what policy will each group choose? c. What is the maximum price that the insurance company can charge on each group if insurance company can tell who is smoker? Suppose that smoking status represents asymmetric information: each individual knows if they are a smoker, but the insurance company does not. c. Is it possible to find a price to make both groups 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 groups to purchase insurance, with one group buying L-policies and one group buying H-policies