Question

16 . Individual Problems 20-4

Suppose that every driver faces a 5% probability of an automobile accident every year. An accident will, on average, cost each driver $14,000. Suppose there are two types of individuals: those with $84,000.00 in the bank and those with $3,500.00 in the bank. Assume that individuals with $3,500.00 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 $84,000.00 in the bank likely   buy insurance, and those with $3,500.00 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.

False

True

Answer 1

Solution

Given that there is a 5% probability of an automobile accident every year and the cost of that accident is $14,000

So,the actuarilly fair price is the expected cost of the event called accident. i.e., 0.05 * 14,000 i.e., $700

So,this is the minimum premium that the insurance companies must charge the customers.

Given that both the kinds of drivers are slightly risk averse.

Drivers with a bank balance of $84,000

Cost incurred for treatment in case of accident (No insurance) =$14,000

Cost incurred for treatment in case of accident (With insurance) = $700 (this is the insurance premium amount)

Drivers with a bank balance of $3500

Cost incurred for treatment in case of accident (No insurance) =$14,000

These drivers have to declare bankruptcy in case they met with accident if  they are not having insurance plan

Cost incurred for treatment in case of accident (With insurance) = $700 (this is the insurance premium amount)

So,without the law,the drivers with $84,000 in their bank account may not opt for the plan if they are risk taking but on the other hand,the drivers with $3500 have no option but to opt for the insurance if they do not want to bear the risk of accident (5% probability)

As discussed above,if the state law is passed,it will effect only the behavior of the drivers having a balance of $84,000 because the ones with a balance $3500 will by default be insured as they very well know that they will not be able to bear the treatment cost without insurance in case of an accident.

Answer : True (since both the kind of drivers are only slightly risk-averse)

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