Question 3 Suppose there are two equal-sized groups of people: smokers and non-smokers. Both types of people have utility U = In(C), where E is the amount of consumption that people haye in any period. So long as they are healthy, individuals will consume their entire income of SEEING. If they need medical attention [and have no insurance], they will have to spend $1l], to get healthy again, leaying them with only S1D, to consume. Smokers have a 12% chance of requiring major medical attention, while nonsmokers have a 256 chance. Insurance companies can sell two types of policies. The "low-deductible\" [Ll policy covers all medical costs above 53,011] while the "high deductible" {H-} policy only coyers medical costs aboye SEND. 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 charge actuarially fair premiums for each policy and group, show that both groups will purchase the L-policy. Now 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 groups to purchase insurance, with one group buying L-policies and one group buying H-policies