Suppose that every driver faces a 1% prob- ability 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 $60,000 in the bank and those with $5,000 in the bank. Assume that individuals with $5,000 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. What is the actuarially fair price of insurance? What price are individuals with $5,000 in the bank willing to pay for the insurance? Will those with $5,000 in the bank voluntarily purchase insurance? What is the effect of state laws forcing individuals to purchase auto liability insurance?

1. Actuarially fair price is $100.

2. The amount those with $5,000 bank balance will be willing to pay is $50.

3. Those with $5,000 bank balance will not voluntarily purchase insurance.

4. This will make every drivers not to have any other choice than to buy auto insurance.

Explanation:

The calculations are done as follows:

1. What is the actuarially fair price of insurance?

Insurance actuarially fair price = expected loss

                                                  = accident probability × Insurance cost

                                                  = 1% × $10,000

                                                  = $10

Therefore, actuarially fair price is $100

2. What price are individuals with $5,000 in the bank willing to pay for the insurance?

Since in the case that the accident happens, individuals with $5000 in bank will lose $5000, the amount they will be willing to pay will be smaller premium calculated as follows:

Amount they are willing to pay = accident probability × bank balance

                                                    = 1% × $5,000

                                                    = $50

Therefore, the amount those with $5,000 bank balance will be willing to pay is $50.

3. Will those with $5,000 in the bank voluntarily purchase insurance?

Since the acturarilly fair price of insurance of $100 is higher than $50 which is the amount those with $5,000 bank balance will be willing to pay, those with $5,000 bank balance will not voluntarily purchase insurance.

4.  What is the effect of state laws forcing individuals to purchase auto liability insurance?

The effect of the state laws forcing individuals to purchase auto liability insurance will make every drivers not to have any other choice than to buy auto insurance. This is because they now have choice to consider the difference between the insurance price and their willingness to pay.

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