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UTILITY AND DECISION MAKING 583

15 The Russo Manufacturing Company must decide whether to manufacture a component
part at its Milan plant or purchase the component part from a supplier. The resulting profit
is dependent upon the demand for the product. The following payoff table shows the
projected profit (in thousands of euros).

State of Nature
Low Demand Medium Demand High Demand
Decision Alternative s 1 s 2 s 3
20 40 100
Manufacture, d 1
Purchase, d 2 10 45 70

The state-of-nature probabilities are P(s 1 ) ¼ 0.35, P(s 2 ) ¼ 0.35 and P(s 3 ) ¼ 0.30.
a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether Russo should attempt to obtain a better estimate of demand.
c. A test market study of the potential demand for the product is expected to report either a
favourable (F)orunfavourable(U) condition. The relevant conditional probabilities are as
follows:

PðF j s 1 Þ¼ 0:10 PðU j s 1 Þ¼ 0:90
PðF j s 2 Þ¼ 0:40 PðU j s 2 Þ¼ 0:60
PðF j s 3 Þ¼ 0:60 PðU j s 3 Þ¼ 0:40

What is the probability that the market research report will be favourable?
d. What is Russo’s optimal decision strategy?
e. What is the expected value of the market research information?
f. What is the efficiency of the information?

16 Three decision makers have assessed utilities for the following decision problem (payoff in euros).

State of Nature
Decision Alternative s 1 s 2 s 3
20 50 20
d 1
80 100 100
d 2

The indifference probabilities are as follows.

Indifference Probability (p)
Payoff Risk Avoider Risk Taker Risk Neutral
100 1.00 1.00 1.00
80 0.95 0.70 0.90
50 0.90 0.60 0.75
20 0.70 0.45 0.60
20 0.50 0.25 0.40
100 0.00 0.00 0.00

For the payoff of 20, what is the premium that the risk avoider will pay to avoid risk? What is
the premium that the risk taker will pay to have the opportunity of the high payoff?

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