Question

There are 200 people of two types on the road: good drivers and bad drivers. Good drivers (G) have a 1% chance of causing an accident while bad drivers (B) have a 5% chance of causing an accident. The proportion of bad drivers is 0.5, so the proportion of good drivers is 0.5. The cost of an accident is $6,000. Good drivers have a willingness to pay for insurance of $200 while bad drivers have a willingness to pay of $400.

a. Suppose the insurance company knows each driver’s type. What premium would the insurance company charge each type of driver? (Assume the insurance company breaks even, so the premium is equal to the expected cost.)

b. Nowsupposethattheinsurancecompanydoesnotknowthedriver’stype. Whatwouldthe insurance company’s expected profit be if it charged premiums based on the individual’s self-reported type?

c. Now suppose that the insurance company does not know the driver’s type. What premiums would the insurance company charge if they did not have any information on the driver’s type? Is there a pooling equilibrium?

Answer 1