There are 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 driver's 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 driver's 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 driver's types?
If you are uncertain whether insurance would be sold, explain why.