4. There are two types of drivers on the road today, Speed Racers with a 5% chance of an accident per year, and Low Riders with a 1% change per year. There are an equal number of Speed Racers and Low Riders. The cost of an accident is $12,000. Assume that there is free entry into the insurance market, the insurers always know the relative shares of each type in the population, and firms are risk-neutral. Assume that your income is $12,000 in the absence of an accident.

a. Suppose an insurance company knows with perfect information each person's type. What premium would they charge each type?

b. Now suppose there is asymmetric information, so the insurance company doesn't know each driver's type with certainty, would insurance be sold if:

1) Drivers self report their types to the company (but the firm knows the share of each type)?

2) The insurance company doesn't know anything about your type (you don't tell them anything). The insurance company still knows the share of each type in the population. If you are not sure about the answer, say why.

c. Suppose that everyone has the same utility function,U(Y) =Y. Suppose that there are two insurance contracts, one costing more than the other, and people buy each contract in equilibrium. Which group would buy the more expensive one and which group would buy the cheaper one? What would be the cost of the more expensive policy?

d. If,U(Y) =Y, would be a premium of $100 for the cheaper policy that covers one fourth of the losses (pays out $3000) allow both contracts to be sold? (Remember, their income is $12,000 if the bad event does not happen.)