An insurance agent (interviewed in Jonathan Clements, “Dare to Live Dangerously: Passing on Some Insurance Can Pay Off,” Wall Street Journal, July 23, 2005, D1) states, “On paper, it never makes sense to have a policy with low deductibles or carry collision on an old car.” But the agent notes that raising deductibles and dropping collision coverage can be a tough decision for people with a low income or little savings. Collision insurance is the coverage on a policyholder’s own car for accidents where another driver is not at fault.
a. Suppose that the loss is $4,000 if an old car is in an accident. During the six-month coverage period, the probability that the insured person is found at fault in an accident is . Suppose that the price of the coverage is $150. Should a wealthy
person purchase the coverage? Should a poor person purchase the coverage? Do your answers depend on the policyholder’s degree of risk aversion? Does the policyholder’s degree of risk aversion depend on his or her wealth?
b. The agent advises wealthy people not to purchase insurance to protect against possible small losses. Why?