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Sequential Decisions 513

successful. The probability of each joint outcome is the product of the probabili-

ties of the individual outcomes because these risks are assumed to be independ-

ent. Thus, the chance that both methods will succeed is (.7)(.2)  .14, and so on.

Note that the probabilities of the four possible outcomes sum to 1, as they must.

When the results of both R&D programs are in, the firm must decide which

method to commercialize. If the biogenetic research effort fails (the lower two

branches), the firm has no choice; it must go the biochemical route. If the bio-

genetic research is successful, the firm should commercialize this method

because it offers the greater profit. (Note that the firm will produce the drug

with only a singlemethod—whichever is more profitable.) Thus, in the upper

two branches, the drug is produced biogenetically. The profit is $200 million

minus $30 million (the total investment on both methods), or $170 million.

The other profit outcomes are computed in analogous fashion.

What is the firm’s expected profit at the start of the simultaneous R&D

effort? Multiplying the possible monetary outcomes by their respective proba-

bilities, we compute this to be

.

Simultaneous development offers a larger expected profit than the next-best

alternative, pursuing the biochemical approach exclusively. By undertaking

both, the firm enjoys the security of biochemical’s “sure thing” profits while

still testing the biogenetic waters—a long shot that could provide a huge profit.

Even in the likely event that the biogenetic option fails, the firm makes a profit.

The decision tree instructs us that pursuing both approaches simultaneously

increases the firm’s expected profit by 72.4  68 $4.4 million vis-à-vis pur-

suing the biochemical method alone.

However, the firm has not yet exhausted its options. Now it considers pur-

suing the R&D methods sequentially: one first, then (if necessary) the other.

This raises an obvious question: Which method should it pursue first?

The decision tree in Figure 12.4 depicts the sequential strategy: biochemical

R&D first, then biogenetic R&D. After the outcome of the first R&D effort is

known, the firm can choose to commercialize it or invest in the second program.

(If the biogenetic program is subsequently pursued and fails, the firm goes back

and completes development of the biochemical approach.) The top square

shows the firm’s decision in the event the biochemical program is successful.

Contrary to one’s intuition, the firm should notproceed to immediate devel-

opment; rather, its best course of action is to invest in the second R&D program,

see the result, and, if it fails, fall back on the biochemical approach. The result-

ing expected profit from making this second R&D investment is $82 million—

$2 million better than from immediately commercializing a biochemically based

drug. What if the biochemical program is less successful? The lower decision

square provides the answer. As we might expect, the firm’s best action is to invest

in the second R&D program; the expected profit of $50 million is $10 million

(.14)(170)(.06)(170)(.56)(60)(.24)(20)$72.4 million

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