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Similarly, he is indifferent to losing$120,000 for certain or a 25–75 risk between

the same two outcomes.^7 Therefore, these utilities are U(200) (.7)(100) 

(.3)(0) 70 and U(120) (.25)(100) (.75)(0) 25.

Now the wildcatter is ready to compare his two options. The expected util-

ity of drilling is (.2)(100) (.18)(70) (.32)(50) (.3)(25) 56.1. The util-

ity of not drilling is U($0) 50. Thus, drilling offers the higher expected utility

and should be elected.^8

WHY THE EXPECTED-UTILITY METHOD WORKS The preceding discussion

shows how the expected-utility rule works. It is also worth checking whyit

works. Part (b) of Figure 12.8 demonstrates the reasoning behind the

expected-utility rule. Beside each monetary outcome is listed an equivalent

(in terms of preference) risk over the best and worst outcomes. By his own

admission, the wildcatter is indifferent to a given monetary outcome versus the

equivalent risk. Therefore, we can substitute the equivalent risk for each mon-

etary outcome in the decision tree. Substituting equivalent risks will not

change how the wildcatter feels about the drill option. (This assumption usu-

ally is called the substitution principle.) We make the substitution by (mentally)

deleting the monetary outcome and, in its place, connecting the equivalent

risk to the branch tip. Although the decision tree looks very bushy, the sub-

stitution has an important implication: Now the only outcomes in the tree are

$600,000 and $200,000, the best and worst outcomes. If we add up the total

probability of obtaining $600,000, we obtain the reduced tree on the right.

The probability is computed as

(Note that four branch paths on the tree end in $600,000. Each path involves

a pair of chance branches, so we use the product rule for probabilities.) Thus,

the actual drilling risk is equivalent (has been reduced) to a simpler risk offer-

ing a .561 chance at $600,000 and a .439 chance at $200,000.

Now the wildcatter’s decision is straightforward: Drilling is preferred to

not drilling because, by his own admission, the wildcatter rates $0 for certain

as equivalent to a .5 chance of the best outcome, and this is less than the .561

equivalent chance offered by drilling. We have gone to some trouble to see

through the logic of the wildcatter’s choice. But notice that applying the

(.2)(1.0)(.18)(.7)(.32)(.5)(.30)(.25).561.

(^7) Notice that -$200,000 is not an actual drilling outcome. (The worst actual outcome is $120,000.)
However, this fact makes no substantive difference in assigning utilities. The wildcatter is free to
assign any outcome as the lowest or “zero-utility” value as long as this monetary outcome is lower
than all actual outcomes.
(^8) We note in passing that the original drilling site and the second drilling site have identical expected
profits: $120,000. (Check the expected value of the second site.) Loosely speaking, the original site
is more risky than the second. (It has a greater upside potential as well as greater downside risk.)
Here the risk-averse wildcatter rejects the first site while choosing to drill the second.
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