9781118041581

As always, marginal analysis offers a direct answer. Additional firms should

be sought as long as the expected marginal benefit (MB) exceeds the extra

cost (MC). From Table 13.3, we find the optimal number to be four in the uni-

form case. (From three to four buyers, MB is $1.2 million and exceeds MC, but

from four to five, MB is less than MC.) The firm’s expected price (net of its

costs) is 59.2  4 $55.2 million. For the normal distribution, in turn, the

optimal number of buyers is five. By experimenting with different search costs,

we can confirm that the lower the cost of search, the greater the number of buy-

ers the firm should seek.

566 Chapter 13 The Value of Information

CHECK

STATION 5

In the preceding example, what would be the effect on the optimal number of buyers if

a typical buyer’s value were uniformly distributed between $46 and $70? (Note that the

expected value of the typical buyer has increased by $6; but the dispersion, that is, stan-

dard deviation, is unchanged.) What would be the effect if a typical buyer’s value were

distributed uniformly between $46 and $58? (Here, the typical buyer’s expected value is

unchanged but the standard deviation has been cut in half.)

The Stock Market and

the Economy

Revisited

As noted at the beginning of the chapter, the stock market has dropped precipitously

prior to all eight postwar recessions. In light of a sustained stock market drop, some ana-

lysts have concluded that there will be a forthcoming recession. Do you agree?

The answer is not a simple “yes.” As a famous economist once said, “The stock mar-

ket has predicted 14 of the last 8 recessions.” Thus, in at least six instances, stock prices

have fallen without a subsequent economic recession. In these cases, stock price move-

ments were a false indicator of the future course of the economy. Thus, a rough estimate

for the chances of a recession given a stock market drop is 8/14 or 57 percent.

Table 13.4a illustrates the point. While the U.S. economy has suffered eight periods

of recession in the postwar period, the norm has been a growing economy. (The table

shows that the economy grew in 32 out of 40 periods, or roughly 80 percent of the time.)

The stock market fell prior to all eight recessions, but it also fell prior to periods of eco-

nomic growth. We see from the second row of Table 13.4 that Pr(Coming recessionƒStock

drop) 8/14, or 57 percent.

Now let’s return to the yacht dealer’s decision introduced in Chapter 12. Recall

that the dealer assessed a .6 chance for a growing economy. This is more pessimistic

than historical experience would suggest. Based on this forecast, the dealer’s optimal

course of action was to order 50 yachts, thereby earning an expected profit of

$175,000. We now can ask, How should the dealer revise this forecast of economic

conditions in light of stock market movements? How many yachts should the dealer

order?

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