Question

4. 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 $13,000. Suppose there are two types of individuals: those with $78,000.00 in the bank and those with $3,250.00 in the bank. Assume that individuals with $3,250.00 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 $78,000.00 in the bank likely (will/will not) buy insurance, and those with $3,250.00 in the bank likely (will/will not) 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 only the behavior of drivers with $3,250.00 in the bank

Answer 1

Actuarilly fair price of insurance = ( Probability of accident ) x ( loss in case the accident occurs )

Actuarilly fair price of insurance = 0.02 x 13000

Actuarilly fair price of insurance = $ 260

Therefore, the actuarilly fair price that the insurance company charges will be $ 260.

Expected cost of accident of the driver with $ 78,000 in his bank account without insurance = ( Probability of accident ) x ( loss in case the accident occurs ) = 0.02*13000 = $ 260

Expected cost of accident of the driver with $ 3250 in his bank account without insurance = ( Probability of accident ) x ( loss in case the accident occurs ) = 0.02*3250 = $ 65 ( Since he can declare bankruptcy and is then required to pay only what is there in his bank account )

As we can see, the expected cost of accident is lower than the price of insurance for the driver with $3250 in his bank account and is equal for the other driver. Therefore, only the drivers with $ 78000 in their bank accounts will choose to purchase insurance.

At this price, drivers with $78,000.00 in the bank likely will buy insurance, and those with $3,250.00 in the bank likely will not buy insurance.

True

The law will affect only the behavior of drivers with $3,250.00 in the bank. It is because the drivers with $ 78000 in the banks would have bought insurance in the absence of the law as well. On the other hand, the drivers with $3250 in their bank accounts would not have bought the insurance if the law had not been passed. Therefore, it would affect only the behavior of drivers with $3,250.00 in the bank.