9781118041581

13. Consider once again the R&D strategies of the pharmaceutical company.
    Suppose the company’s management is risk averse and has assessed the
    following utility values for the set of possible outcomes (in millions of dollars).

Outcome Utility Outcome Utility

$200 100 $70 59

180 95 60 55

170 92 50 50

100 71 40 44

80 64 20 32

00

Compute the expected utility of pursuing the biochemical approach

alone. Next, find the expected utility of pursuing the biogenetic approach

first, then continuing with the biochemical approach if necessary. In light

of these calculations, what action do you recommend for the company?

How has the company’s risk aversion influenced its decision?

14. In attempting to quantify its attitude toward risk, top management of the
    pharmaceutical company has reported certainty equivalent values for a
    variety of 50–50 risks. These are summarized in the following table.

Outcome of 50–50 Risk Certainty Equivalent

$200 and $0 $ 50

$200 and $50 112

$50 and $0 13

$200 and $112 153

$112 and $50 70

$50 and $13 28

$112 and $13 50

For instance, the company’s CE for a 50–50 risk between $200 million

and $0 is $50 million, and so on.

a. Use these responses to determine utility values for each of the monetary

values in the second column. (Hint:Set U($200) 100 and U($0) 0.

Show that U($50) 50, U($112) 75, and so on.) Construct a utility

graph by plotting points and drawing a smooth curve. (You may wish to

check the utility values in Problem 13 against your curve.)

*b. Consider the mathematical utility function , where U is the

utility value corresponding to monetary outcome y. Check that this

function is an accurate description of the pharmaceutical company’s

attitude toward risk. Is the company very risk averse?

U7.1 1 y

538 Chapter 12 Decision Making under Uncertainty

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