Daniel l. Rubinfeld

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162 Part 2 Producers, Consumers, and Competitive Markets positively correlated HaYing a tendency to move in the same dire~tion. An individual who invests all her money in a single stock (Le" puts all her eggs in one basket) is therefore taking much more risk than is necessary. Risk can be reduced-although not eliminated-by investing in a portfolio of ten or twenty different stocks, Equivalently, you can diversify by buying shares in illUtu;/ funds: organizations that pool funds of individual investors to buy a large number of different stocks. In the case of the stock market, not all risk is diversifiable, Although some stocks go up in price '"vhen others go dO'wn, stock prices are to some extent posi. tively correlated: they tend to move in the same direction in response to changes in economic conditions. For example, the onset of a severe recession, 'which is likely to reduce the profits of many companies, may be accompanied by a decline in the overall market. EYen vvith a diversified portfolio of stocks, therefore, you still face some risk Insurance We have seen that risk-averse people are willing to pay to avoid risk In fact, if the cost of insurance is equal to the expected loss (e,g" a policy with an expected loss of 51000 '"vill cost $1000), risk-averse people will buy enough insurance to recover fully from any financial losses they might suffer, Why The answer is implicit in our discussion of risk aversion, Buyill.g insurance assures a person of having the same income whether or not there is a 10s5. 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 ,'\'ill suffer a $10,000 loss, Let's assume he has 550,000 worth of property, Table 5,6 shows his wealth in two situationswith insurance costing $1000 and without insurance, Note that expected ,,\'ealth is the same (549,000) in both situations, The variability, however, is quite different: As the table shows, with no insurance the standard deviation of wealth is $3000, whereas 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 59000 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, Large Consumers usually buy insurance from companies that specialize in selling it. Insurance companies are finns that offer insurance because they know that when they sell a large number of policies, INSURANCE BURGLARY (PR = .1) NO BURGLARY (PR = .9) EXPECTED WEALTH STANDARD DEVIATION No 40,000 50,000 49,000 3,000 Yes 49,000 49,000 49,000 0 they face relatively little risk The ability to a\-oid risk by operating on a large scale is based on the law of large l1ui/lbers, which tells us that although single events may be random and largely unpredictable, the a\'erage outcome of many similar e\'en~s can be, predicted, For example, I may not be able to predi~t whether a com toss w11l come out heads or tails, but I know that when manv coins are Hipped, approximately half \vill turn up heads and half tails, Likewis~, if I am selling automobile insurance, I carmot predict whether a particular driver will have an accident, but I can be reasonably sure, judging from past experience, about hmv many accidents a large group of drivers will have, By operating on a large scale, insurance companies can assure ~he,mse~ves that over a sufficiently large number of events, total premiums paId m 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 vvill be burgled; if it is, he 'will suffer a 510,000 loss. Prior to faci;g this risk, he calculates the expected loss to be 51000 (.10 x $10,000), There is, however, substantial risk involved, because there is a 10-percent probability of a larae loss, Now suppose that 100 people are similarly situated and that ~ll of the~n buy burglary ll:s,urance from an insurance company. Because they all face a 10- percent probab1~1ty of a 510,000 loss, the insurance company might charge each of them a premiUm of 51000, nlis $1000 premium generates an insurance fund of $100,000 from which losse~ can be paido The insurance company can rely on the law of large numbers, whIch holds that the expected loss to the 100 ll1dividual: 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 10sll1g more than that. When the insurance premium is equal to the expected payout, as ll1 the example abo\'e, we say that the ll1surance is actuarially fair. Because they must cover administrative co~ts and make some profit, however, insurance cor~panies 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 achlarially fair levels, In some states, however, ll1surance premiums are regulated, ~sually :he objective is to protect consumers from "excessive" premiums, We wIll examme government regulation of markets in detail ll1 Chapters 9 and 10 of this book S upp,se a family is buyin~ its first house, They know that to close the sale, they 11 need a deed that gIVes them 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 is rnore likely to be l.maware of the exact nature of his or her ownership rights, For example, the owner may have borrowed heavily, using the house as "collateral" for the loan, Or the property might carry with it a legal requirement that limits the use to which it maybe put Su~pose our family is willing to pay $200,000 for the house but believes 1S a one-in-twenty chance that careful research will reveal that the seller 1:0t achla11y own the property, The property would then be worth noth It there were no insurance available, a risk-neutral family would bid at Chapter 5 Choice Under Uncertainty 63 actuarially fair Situation in which an insurance premium is equal to the expected payout
164 Part 2 Producers, Consumers, and Competitive Markets Chapter 5 Choice Under Uncertainty 65 value of complete information Difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. most 5190,000 for the property (.95[$200,OOOJ + .05[0]) .. However, a familv that expects to tie up most of its assets in a house ,·vould probably be risk avers~ and, therefore, bid much less to buy the house-say, 5150,000. 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 ov\'nership. The buyer does this by purchasing "title insurance./I 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. Because the title insurance company is a specialist in such insurance and can collect the relevant information relatively easily, the cost of title insurance is often less than the expected value of the loss involved. A fee of $1,000 for title insurance is not tU1Usual, and the expected loss can be substantially higher. It is also in the interest of sellers to provide title insurance, because all but the most risk-loving buyers will pay rnuch more for the house \vhen it is insured than when it is not. In fact, most states require sellers to provide title insurance before a sale can be completed. In addition, because mortgage lenders, too, are concerned about such risks, they usually require new buyers to have title insurance before they will issue a mortgage. The Value of Information People often make decisions based on limited information. If more information were available, one could make better predictions and reduce risk Because information is a valuable commodity, people will pay for it. The value of com· plete information is the difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. To see hmv valuable information can be, suppose you are a store manager and must decide hmv many suits to order for the fall season. If you order 100 suits, your cost is $180 per suit. If you order only 50 suits, your cost increases to $200. You knmv that you \,,·ill be selling suits for 5300 each, but you are not sure what total sales will be. All suits not sold can be returned, but for only half of what you paid for them. Without additional information, you will act on your belief that there is a .5 probability that 100 suits \,,·ill be sold and a .5 probability that sales will be 50. Table 5.7 gives the profit that you would earn Ul. each of these two cases. Without additional information, you would choose to buy 100 suits if you were risk neutral, taking the chance -that your profit might be either $12,000 or $1500. But if you 'were risk averse, you might buy 50 suits: In that case, you would know for sure that your profit would be $5000. With complete information, you can place the correct order regardless. of future sales. If sales were going to be 50 and you ordered 50 suits, your protits lId be 55000. If, on the other hand, sales were going to be 100 and you WOl.. • dered 100 suits, your profits would be $12,000. Because both outcomes are or uallv likely, your expected profit with complete information would be 58500. ~e v~lue of information is computed as Less: Expected value with complete information: 58500 Expected value with uncertaulty (buy 100 suits): Value of complete information -56750 51750 Thus it is 'worth paying up to 51750 to obtain an accurate prediction of sales. Even though forecasting is ulevitably imperfect, it may be worth investing in a marketing study that provides a reasonable forecast of next year's sales. Historically, the U.s. dairy industry has allocated its advertising expenditures more or less uniformly throughout the year9 But per capita consumption of milk has declined over the years-a situation that has stirred producers to look for new sh'ategies to encourage milk consumption. One sh'ategy would be to uKrease advertisulg expenditures and to contu1Ue advertising at a lU1iform rate throughout the year. A second sh'ategy would be to invest in market research in order to obtain more information about the seasonal demand for milk; marketers could then reallocate expenditures so that ad\'ertising was most intense when the demand for milk vvas greatest. Research into milk demand shows that sales follovv a seasonable pattern, with demand greatest during the spring and lowest during the summer and early fall. The price elasticity of milk demand is negati\"e but small and the income elasticity positive and large. Most important is the fact that milk advertising has the most effect on sales when consumers have the strongest preference for the product (March, April, and May) and least when preferences are weakest (August, September, and October). In this case, the cost of obtauling seasonalulformation about rnilk demand is relatively low and the value of the information substantial. To estimate this value, we can compare the actual sales of milk durulg a typical year with sales levels that would have been reached had advertising expenditures been made in proportion to the strength of seasonal demand. In the latter case, 30 percent of the advertising budget would be allocated in the first quarter of the year and only 20 percent Ul the third quarter. Making these calculations for the New York metropolitan area shows that the value of information-the value of the additional annual milk sales-was about S4 million. This figure corresponds to a 9-percent increase Ul the profit to producers. In §-t-t, we define the price elasticit~· of demand as the percentage change in quantity demanded resulting from a I-percent change in the price of a good !~ I ~ SALES OF 50 SALES OF TOO EXPECTED PROFIT Buy 50 suits 5,000 Buy 100 suits 1,500 5,000 12,000 5,000 6,750 Q . This example is based on Henry Kinnucan and Olan D. Forker, "Seasonality in the Consumer Response to Milk Advertising with Implications for lv!ilk Promotion Policy," AlIlcricall JOlll'lwi of Agnwltllmi Ecollomics 68 (1986): 562-71
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Daniel l. Rubinfeld

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