There are two types of drivers: reckless drivers (probability of getting into a car accident is 3%, with an estimated car damage of $6000), and careful drivers (probability of an accident is 2%; estimated damage is $5000). The average price of a car is $20,000. The insurance company cannot distinguish between the two types of drivers when they purchase their insurance policy. It, therefore, offers two different insurance policies (two packages) as follows:

Policy A: premium is $75, coverage is $4000

Policy B: premium is $50, coverage is $3000

The utility function (from having wealth/money/asset of ), of all drivers, is given by () = .

a. Which insurance policy (if any) would a reckless driver prefer? Why?

b. Which insurance policy (if any) would a careful driver prefer? Why?

c. What is the maximum premium that a reckless driver would pay for a full-coverage policy? What is the maximum premium that a careful driver would pay for a full-coverage policy?