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Risk Aversion 523

Instead, he seeks to determine a criterion for choosing among risky prospects

that reflects his own attitude toward risk. We now show how he can construct

a utility function that measures his own degree of risk aversion and how he can

use this function to guide his choices.

The wildcatter begins by attaching a utility value to each possible monetary

outcome. Let’s start with the decision to drill. Here the outcomes are $600,000

and -$200,000; these are the best and worst possible outcomes, respectively.

The wildcatter is free to set these utility values arbitrarily as long as the best

outcome receives the higher value. The usual choice is to assign the worst out-

come a utility value of zero. Thus, we would write U(200) 0; that is, the

utility associated with a loss of $200,000 is zero. In turn, let’s arbitrarily set

U(600) 100. This establishes a range of utility values from 0 to 100 for mon-

etary outcomes between the worst and best possible outcomes.

Using these utility values, the wildcatter evaluates the option to drill by

computing its expected utility. The expected utilityis the probability of each

outcome times its utility, summed over all outcomes. Thus, the expected util-

ity of drilling is

Now consider the “do not drill” option. In this case, the wildcatter’s monetary

result is $0 for certain. What utility value should the wildcatter assign this out-

come? To determine U(0), the wildcatter compares $0 for certain with a gamble

offering $600,000 (with probability p) and $200,000 (with probability 1 p).

The wildcatter measures his relative preference for $0 by finding the proba-

bility, p, that leaves him indifferent to the options of $0 and the gamble.

Suppose that, after some mental trial and error, he judges his indifference

probability to be p  .5; that is, he is indifferent to a certain $0 and to a 50–50

(.4)(100)(.6)(0)40.

E(Udrill)(.4)U(600)(.6)U(200)

FIGURE 12.7

The Wildcatter’s

Drilling Problem

Revisited

Given his degree of

risk aversion, the

wildcatter chooses

not to drill.

Do not drill

Drill

Wet

Dry

$0

$600

–$200

.4

.6

(100)

(0)

(50)

40

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