4. You have an old car, and the Bluebook value is $5,000, and you value
the car at this price. You are considering whether you should insure your
vehicle, in case it is damaged. You guess that the probability of your car
being damaged over the next year is 10%. If your car is damaged, and
you are insured, the insurance company would just pay you the Bluebook
value instead of fixing it since it is old.
a. If half of drivers are like you, and expect an accident with 10% prob-
ability, but the other half of drivers with old cars worth $5,000 are
more dangerous, and expect an accident over the next year with 20%
probability, and the insurance company cannot differentiate, what do
they charge customers with old cars to break even?
2
b. What is the expected value of the insurance to you?
c. Your disposable income for the year is $10,000. Your utility over
consumption is $U(c) = c^{1/2}$. What is your expected utility if you
purchase the insurance at the rate from part (a)?
d. What is your expected utility if you do not purchase the insurance?
Do you purchase the car insurance?
e. Does the risky driver with accident probability 20% purchase the
insurance if the price is that of part (a)? Assume they have the same
income as you.
f. What is the maximum price you (the safe driver) are willing to pay
for car insurance?
g. What ratio of safe to risky drivers would make the price from part
(f) feasible for the insurance company?
