9781118041581

The Value of Additional Alternatives 567

From Table 13.4a, we have Pr(Stock dropƒComing recession) 8/8 1.0, Pr(S ƒG) 

26/32  .8125, and Pr(S-ƒG) 6/32  .1875. Using this information, we construct part

(b) of the table. Note that the table is based on the dealer’s prior probability, Pr(G)  .6.

The upper-left entry lists the joint probability that stocks rise (S ) and the economy

grows (G). This is computed as

Pr(S&G) Pr(S ƒG)Pr(G) (.8125)(.6) .4875.

Similarly,

Pr(S&G) Pr(S ƒG)Pr(G) (.1875)(.6) .1125.

The second column is self-explanatory. We can readily compute revised probabilities from

part (b) of the table:

Pr(GƒS) .4875/.4875) 1.0

and

Pr(GƒS) .1125/.512) .22.

The decision tree in Figure 13.4 completes the solution. In light of a rising stock

market, there is no chance of a recession. Accordingly, the dealer should order 100 yachts,

anticipating an expected profit of $350,000. If the stock market falls, there is a 78 percent

chance of a recession. The best the dealer can do is to order 50 yachts, earning an

expected profit of $127,500. Averaging the cases of rising and falling stock prices, the

TABLE 13.4

The Stock Market as a

Leading Indicator

of the Economy

(a) The Historical Record Economy Grows (G) Recession (R) Total

Stocks Rise (S) 26 0 26

Stocks Drop (S) 68 14

Total 32 8 40

(b) The Yacht Dealer’s Economy Grows (G) Recession (R) Total

Assessed Probabilities

Stocks Rise (S) .4875 0 .4875

Stocks Drop (S) .1125 .4 .5125

Total .6000 .4 1.0000

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