Suppose that every driver faces a 1% probability of an automobile accident every

Question

Suppose that every driver faces a 1% 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 $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 bank-ruptcy, 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?

Need 100 words or more please. Thank you

Explanation / Answer

To the insurance company that sells the insurance, there is a .01 probability that it will have to pay $10,000 in compensation and 0.99 probability that it will not have to pay any compensation. So the expected value of compensation is $100 [=0.01(10000) + 0.99(0)]. The expected value of the compensation to be paid by the insurance company is the actuarially fair price of the insurance.

For the individuals that have $5,000 in their bank account, the probability is 0.01 that they will lose $5,000 and 0.99 that they will lose nothing. So their expected loss is $50 [=0.01(5000) + 0.99(0)]. To get their risk subsumed by the insurance company, these inviduals will be ready to pay $50.

But these inviduals won;t voluntarity purchase insurance because insurance companies wont charge less than $100 and the value of this insurance to these individuals is only $50.

If state laws force these individuals to purchase auto liability insurance, then the total costs of the accident will be internalzed and the market outcome will be considered socially optimal. Apart from that, the costs will also fall on these individuals (i.e., drivers), who are here the responsible units of any accident.

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