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 2 types of individuals:those w/$60,000 in the bank and those with $5000 in the bank. Assume that individuals w/$5000 in the bank declare bankruptcy if they get in a an accident. In bankruptcy, creditors receive only what individuals have in the bank. 1. What is the actuarially fair price of insurance? 2.What price are individuals w/$5000 in the bank willing to pay for the insurance?3. Will those w/$5000 in the bank voluntarily purchase insurance?

Explanation / Answer

High-Risk Consumers: They have a 20% chance of losing $2000. Since they're risk-averse, they value full insurance at $1000 ($600 more than the actuarially fair premium of $400). Low-Risk Consumers: They have a 1% chance of losing $2000. Since they're risk-averse, they value full insurance at $50 ($30 more than the actuarially fair premium of $20). If insurance companies can't distinguish High- from Low-Risk consumers, an actuarially fair premium for an average consumer would cost .5*$400+.5*$20=$210. If consumers purchase insurance voluntarily, though, the Low-Risk will drop out of the market - they won't pay $210 to get a policy worth $50 to them. With only High-Risk consumers in the market, the competitive price of a policy is $400. The market fails to realize $30 worth of consumer surplus per Low-Risk consumer.

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