There are two types of drivers on the road today: Speed Racers have a 5% chance of causing an accident per year, and Low Riders have a 1% chance of causing an accident per year. There are equal numbers of Speed Racers and Low Riders in the population. The cost of an accident is $12,000.

Suppose an insurance company knows with certainty each driver’s type. What premium would the insurance company charge each type of driver if prices are actuarially fair?

Now suppose that there is asymmetric information so that the insurance company does not know with certainty the driver’s type. Describe the insurance contracts that would be offered if no information at all is known about individual driver’s types. What if drivers self-reported their types to the insurance company?