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584 CHAPTER 13 DECISION ANALYSIS

17 In Problem 16, if P(s 1 ) ¼ 0.25, P(s 2 ) ¼ 0.50 and P(s 3 ) ¼ 0.25, find a recommended
decision for each of the three decision makers. Note that for the same decision problem,
different utilities can lead to different decisions.
18 A firm has three investment alternatives. The payoff table (in thousands of euros) and
associated probabilities are as follows:

Economic Condition
Investment Up Stable Down
100 25 0
d 1
d 2 75 50 25
d 3 50 50 50
Probabilities 0.40 0.30 0.30

a. Using the expected value approach, which decision is preferred?
b. For the lottery having a payoff of E100 000 with probability p and E0 with probability
(1 p), two decision makers expressed the following indifference probabilities:

Indifference Probability (p)

Profit Decision Maker A Decision Maker B
E75,000 0.80 0.60
50,000 0.60 0.30
25,000 0.30 0.15

Find the most preferred decision for each decision maker using the expected utility
approach.
c. Why don’t decision makers A and B select the same decision alternative?

19 Zondo Industries is considering purchasing an insurance policy for its new office
building in Port Elizabeth. The policy has an annual cost of E10 000. If Zondo
Industries does not purchase the insurance and minor fire damage occurs to the office
building, a cost of E100 000 is anticipated; the cost if major or total destruction occurs
is E200 000. The payoff table in (E), including the state-of-nature probabilities, is as
follows:

Damage
None Minor Major
Decision Alternative s 1 s 2 s 3
10 000 10 000 10 000
Purchase insurance, d 1
0 100 000 200 000
Do not purchase insurance, d 2
Probabilities 0.96 0.03 0.01

a. Using the expected value approach, what decision do you recommend?
b. What lottery would you use to assess utilities? (Note: The data are costs, which makes
the best payoff E0.)

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