$5.$ Individual Problems $20-4$

Suppose that every driver faces a $2\%$ probability of an automobile accident every year. An accident will, on average, cost each driver $$10,000.$ Suppose there are two types of individuals: those with $$50,000\mathrm{.}00$ in the bank and those with $$2,500\mathrm{.}00$ in the bank. Assume that individuals with $$2,500\mathrm{.}00$ in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse.

In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is

$.$

Assume that the price of insurance is set at the actuarially fair price.

At this price, drivers with $$50,000\mathrm{.}00$ in the bank likely$$buy insurance, and those with $$2,500\mathrm{.}00$ in the bank likely$$buy insurance. $($Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.$)$

Suppose a state law has been passed forcing all individuals to purchase insurance at the actuarially fair price.

True or False: The law will affect the behavior of both types of drivers.

True

False