In the state of Oklahoma the Sooner Insurance Company has noticed the following two differences between men and women drivers:

Men are more likely to have driving accidents: the probability that a man has a car accident is 25% and the probability that a woman has an accident is 19%.

When a man has an accident the damage is likely to be higher: the average damage to a $15,000 car driven by a man is $7500 (so the car is only worth $7500 after the accident) and only $3600 if driven by a woman (so the car is worth only $11,400).

In addition the firm knows that men are willing to pay at most $2343.75 for a full insurance policy. Women are willing to pay at most $745.50 for a full insurance policy. Drivers are equally divided between men and women.

a) What is the cost of providing full fair insurance for men? Given the information provided above will men purchase this policy? What is the cost of providing full fair insurance for women? Will women purchase this policy?

b) What is the expected value of a $15,000 car driven by a man? Given their willingness to pay for full insurance what is the certainty equivalent value of the car? What is the risk premium that they are willing to pay? Illustrate the expected value, the certainty equivalent and the risk premium in a diagram.

c) What is the expected value of a $15,000 car driven by a woman? Given their willingness to pay for full insurance what is the certainty equivalent value of the car? What is the risk premium that they are willing to pay? Illustrate the expected value, the certainty equivalent and the risk premium in a diagram.

Suppose that the state government passes anti-discrimination legislation and requires that insurance companies offer policies at the same price per dollar of coverage to both men and women.

d) Suppose that the firm offers only a single price per dollar of coverage and allows individuals to buy insurance to fully insure against their losses. Show that the firm cannot offer a single price for insurance that does not lose money and is acceptable to both men and women.

e) Given your answer to (c) what policy will the firm offer? Who will be covered men or women?