(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 198

CHAPTER 5 • Uncertainty and Consumer Behavior 173

a large loss. Now suppose that 100 people are similarly situated and that all of
them buy burglary insurance from the same company. Because they all face a
10-percent probability of a $10,000 loss, the insurance company might charge
each of them a premium of $1000. This $1000 premium generates an insurance
fund of $100,000 from which losses can be paid. The insurance company can
rely on the law of large numbers, which holds that the expected loss to the 100
individuals as a whole is likely to be very close to $1000 each. The total payout,
therefore, will be close to $100,000, and the company need not worry about losing more than that.
When the insurance premium is equal to the expected payout, as in the example above, we say that the insurance is actuarially fair. But because they must
cover administrative costs and make some profit, insurance companies typically charge premiums above expected losses. If there are a sufficient number of
insurance companies to make the market competitive, these premiums will be
close to actuarially fair levels. In some states, however, insurance premiums are
regulated in order to protect consumers from “excessive” premiums. We will
examine government regulation of markets in detail in Chapters 9 and 10 of this
book.
In recent years, some insurance companies have come to the view that catastrophic disasters such as earthquakes are so unique and unpredictable that
they cannot be viewed as diversifiable risks. Indeed, as a result of losses from
past disasters, these companies do not feel that they can determine actuarially
fair insurance rates. In California, for example, the state itself has had to enter
the insurance business to fill the gap created when private companies refused to
sell earthquake insurance. The state-run pool offers less insurance coverage at
higher rates than was previously offered by private insurers.

• actuarially fair
Characterizing a situation in
which an insurance premium is
equal to the expected payout.

EX AMPLE 5. 3 THE VALUE OF TITLE INSURANCE WHEN BUYING A HOUSE

Suppose you are buying your
first house. To close the sale, you
will need a deed that gives you
clear “title.” Without such a clear
title, there is always a chance that
the seller of the house is not its
true owner. Of course, the seller
could be engaging in fraud, but
it is more likely that the seller is
unaware of the exact nature of his or her ownership
rights. For example, the owner may have borrowed
heavily, using the house as “collateral” for a loan. Or
the property might carry with it a legal requirement
that limits the use to which it may be put.
Suppose you are willing to pay $300,000 for
the house, but you believe there is a one-in-twenty
chance that careful research will reveal that the seller
does not actually own the property. The property

would then be worth nothing. If
there were no insurance available,
a risk-neutral person would bid at
most $285,000 for the property
(.95[$300,000] + .05[0]). However,
if you expect to tie up most of your
assets in the house, you would
probably be risk averse and, therefore, bid much less—say, $230,000.
In situations such as this, it is clearly in the interest of the buyer to be sure that there is no risk of a
lack of full ownership. The buyer does this by purchasing “title insurance.” The title insurance company researches the history of the property, checks
to see whether any legal liabilities are attached

to it, and generally assures itself that there is no
ownership problem. The insurance company then
agrees to bear any remaining risk that might exist.