Question

Suppose that every driver faces a 4% 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 $104,000.00 in the bank and those with $6,500.00 in the bank. Assume that individuals with $6,500.00 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 $6,500.00 in the bank likely (will/will not) buy insurance, and those with $104,000.00 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 $6,500.00 in the bank.

Answer 1

Actuarially fair price = 4% of $13,000

                              = (4 / 100) * $13000

                              = $520

Explanation:

To the insurance company that sells the insurance, there is a 0.04 probability that it will have to pay $13,000 in compensation and 0.96 probability that it will not have to pay any compensation. So the expected value of compensation is $520 [=0.04(13000) + 0.96(0)].

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will not buy insurance because now the price of insurance is $520 but their expected loss is only $260 so they are not willing to buy insurance.

Explanation:

For the individuals that have $6500 in their bank account, the probability is 0.04 that they will lose $6500 and 0.96 that they will lose nothing.

So their expected loss is $260 [=0.04(6500) + 0.96(0)].

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will buy insurance because now the price of insurance is $520 as the expected loss is 104000*4% = $4160 so as the insurance price is less than expected cost without insurance. he will buy the insurance.

True because at the actuarially fair price of $520, the drivers with $6,500 in bank will not voluntarily purchase the insurance. So this causes him to  purchase insurance at the actuarially fair price unwillingly.