1. Two types of drivers on the road today. Speed Racers have a 5% chance of causing an accident per year, while Low Riders have a 1% chance of causing an accident per year. There are the same number of Speed Racers as there are Low Riders. The cost of an accident is $12,000.

(a) Suppose an insurance company knows with certainty each drivers type. What premium would the insurance company charge each type of driver?

(b) Now suppose that there is asymmetric information so that the insurance company does not know with certainty the drivers type. Would insurance be sold if

i. drivers self-reported their types to the insurance company?ii. no information at all is known about individual drivers types?

2. Rose's preference is represented by the utility function U = ln(2C) where C isthe amount of consumption she has in any given period. Her income is 40,000 dollars peryear and there is a 2% chance that she will be involved in a catastrophic accident that willcost her 30,000 dollars next year.

(a) What is her expected utility?

(b) Calculate an actuarially fair insurance premium. What would her expected utility be was she to purchase the actuarially fair insurance premium?

(c) What is the most that she would be willing to pay for insurance, given her utility function?

3. Chimnesia has two equally 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 tospend 10,000 to get healthy again, leaving them with only 5,000 to consume. Smokers havea 12% chance of requiring major medical attention, while non- smokers have a 2% chance.Insurance companies in Chimnesia can sell two types of policy. The low deductible (L-)policy covers all medical costs above 3,000, while the high deductible (H-) policy only coversmedical 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 nonsmoker and charges the actuarially fair premiums for each policy and group, show that both groups will purchase the L-policy.

(c) Suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn't. Explain whyit is impossible, at any prices, 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) Suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn't. Show that it ispossible for both groups to purchase insurance, with one group buying L-policies and one group buying H-policies.