(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 197

172 PART 2 • Producers, Consumers, and Competitive Markets
Why? The answer is implicit in our discussion of risk aversion. Buying insurance assures a person of having the same income whether or not there is a loss.
Because the insurance cost is equal to the expected loss, this certain income is
equal to the expected income from the risky situation. For a risk-averse consumer, the guarantee of the same income regardless of the outcome generates
more utility than would be the case if that person had a high income when there
was no loss and a low income when a loss occurred.
To clarify this point, let’s suppose a homeowner faces a 10-percent probability that his house will be burglarized and he will suffer a $10,000 loss. Let’s
assume he has $50,000 worth of property. Table 5.6 shows his wealth in two situations—with insurance costing $1000 and without insurance.
Note that expected wealth is the same ($49,000) in both situations. The variability, however, is quite different. As the table shows, with no insurance the
standard deviation of wealth is $3000; with insurance, it is 0. If there is no
burglary, the uninsured homeowner gains $1000 relative to the insured homeowner. But with a burglary, the uninsured homeowner loses $9000 relative to
the insured homeowner. Remember: for a risk-averse individual, losses count
more (in terms of changes in utility) than gains. A risk-averse homeowner, therefore, will enjoy higher utility by purchasing insurance.
THE LAW OF LARGE NUMBERS Consumers usually buy insurance from
companies that specialize in selling it. Insurance companies are firms that
offer insurance because they know that when they sell a large number of policies, they face relatively little risk. The ability to avoid risk by operating on
a large scale is based on the law of large numbers, which tells us that although
single events may be random and largely unpredictable, the average outcome
of many similar events can be predicted. For example, I may not be able to
predict whether a coin toss will come out heads or tails, but I know that when
many coins are flipped, approximately half will turn up heads and half tails.
Likewise, if I am selling automobile insurance, I cannot predict whether a
particular driver will have an accident, but I can be reasonably sure, judging from past experience, what fraction of a large group of drivers will have
accidents.
ACTUARIAL FAIRNESS By operating on a large scale, insurance companies
can be sure that over a sufficiently large number of events, total premiums
paid in will be equal to the total amount of money paid out. Let’s return to
our burglary example. A man knows that there is a 10-percent probability that
his house will be burgled; if it is, he will suffer a $10,000 loss. Prior to facing
this risk, he calculates the expected loss to be $1000 (.10 ϫ $10,000). The risk
involved is considerable, however, because there is a 10-percent probability of

TABLE 5.6

THE DECISION TO INSURE ($)

INSURANCE

BURGLARY
(PR ‫ ؍‬.1)

NO BURGLARY
(PR ‫ ؍‬.9)

EXPECTED
WEALTH

STANDARD
DEVIATION

No

40,000

50,000

49,000

3000

Yes

49,000

49,000

49,000

0