9781118041581

Keefer, D. L., C. W. Kirkwood, and J. L. Corner. “Perspective on Decision Analysis Applications,

1990–2001.” Decision Analysis. (March 2004): 4–22.

Internet sites dealing with decision making under uncertainty include

Sam Savage’s wonderful guide to risk at http://www.analycorp.com/uncertainty/, and

decision-tree software published by Decision Support Services, http://www.treeplan.com/.

540 Chapter 12 Decision Making under Uncertainty

CHECK STATION

ANSWERS

1. The firm’s expected profit under the private contract is (.25)($2) 
   (.41)($.7) (.34)($.5) $.617 million. Under the government contract,
   the firm’s expected profit is (.45)($4) (.55)($2.5) $.425 million. In
   terms of expected value, the private contract is the better alternative.


2. The executive’s expected profit of drilling to only3,000 feet is (.4)(600) 
   (.6)(160) $144 thousand. By quitting after 3,000 feet, the executive
   takes a loss of $160,000. What is her expected profit it she drills deeper? It
   is (.2)(400) (.8)(250) $120 thousand. The expected loss from
   drilling deeper is smaller than that from quitting. Finally, the expected
   profit from drilling 5,000 feet (if necessary) is (.4)(600) (.6)(120) 
   $168 thousand. This is the executive’s best course of action.


3. We calculate firm A’s expected profit from launching the product in two
   steps. If firm B brings out its own product (probability 60 percent), A’s
   expected profit is (.5)($10) (.5)($30) $10 million. If B does not
   bring out a product (probability 40 percent), A’s profit is $20 million. Thus,
   firm A’s overall expected profit is (.4)($20) (.6)($10) $2 million. To
   maximize expected profit, the firm should launch the product.


4. The expected utility of a 50–50 risk between $600,000 (U 100) and $0
   (U 50) is (.5)(100) (.5)(50) 75. From Figure 12.9, we see that the
   CE of this risky prospect is about $220,000. In contrast, the expected value
   of this risk is $300,000. To determine this expected value using the figure,
   draw a line between the $600,000 and $0 points on the graph. Then find
   .75 on the utility scale, read over to the line, and read down to the
   monetary value of $300,000. Note that the risk discount (the horizontal
   gap between the utility curve and the dashed line) is smaller here than for
   the $600,000 versus $200,000 risk. This illustrates a general principle:
   The smaller the range of risk, the closer the CE is to the expected value.

Con Edison

Revisited

What decision did the Con Ed operator take, and what was the result? The oper-

ator initially attempted to reroute power, thinking that only one transmission

line was down. He also reduced voltage and called for added emergency power

from city generators. About 30 minutes into the emergency, he shed about

25 percent of the system’s load. Unfortunately, this proved to be too little, too

late. Eleven minutes after load was shed, New York City blacked out completely.

It took 25 hours to restore power to all parts of the city.

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