Suppose there are two types of drivers on the road. Speed Racers have a 7% chance of causing an accident per year, while Low Riders have a 2% 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 $20,000.
a. Suppose the insurance companies know with certainty each driver’s type. What would be the actuarially fair premium that the company would charge each type of driver?
b. Now suppose there is asymmetric information so that the insurance company does not know with certainty each driver’s type. What will happen if the insurance company asks drivers to self-report their type?
c. What will happen if the insurance company admits that it has no idea which drivers are Speed Racers and offers one insurance plan at a price that is based on the average risk across all drivers? Explain the problem of adverse selection in this context.