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Decisions under Uncertainty

Most choices people make involve some amount of uncertainty about the possible consequences. For example, every time a person gets into a car, there is a risk of an accident's causing harm to the person or to other people. People nevertheless continue to drive because the benefits exceed the expected costs. The value of driving is enhanced, however, if the cost of accidents can be reduced or the risk can be spread efficiently. The first possibility, reducing accident costs, involves prevention. To be sure, drivers have an incentive to invest in some prevention to lower their own risk, but they may fail to take account of the risk that they impose on others (pedestrians or other drivers). Laws against speeding, safety regulations, and the risk of liability for damages in torts provide the necessary additional incentives.

Some accidents are inevitable, however, even when people engage in optimal prevention. In this case, the adverse effects of accidents can be mitigated by insurance. Market insurance operates on the principle that individuals are averse to risk (that is, they dislike unpredictable fluctuations in their income) and hence are willing to pay something to avoid it. For example, if the probability of an automobile accident in a given year is one in one hundred and the loss from an accident is $10,000, then the expected loss is $10,000/100 = $100. A risk-averse person would be willing to pay more than $100 per year in return for an insurance company's promise to cover the $10,000 loss in the event of an accident. The insurance company is willing to make this promise because by selling a large number of policies, it can predict with a high degree of accuracy the number of claims that it will face (owing to the law of large numbers), thus enabling it to earn a profit. (In the above example, sale of one thousand policies at $120 each produces an average of ten claims a year and expected profit of $20,000.) The pervasiveness of insurance attests to the mutual benefits that it provides to insurers and their customers.

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