9781118041581

Risk Aversion 527

Expected Utility and Risk Aversion

Figure 12.9 shows the wildcatter’s utility curve over a range of monetary out-

comes. This curve is constructed by plotting utilities for particular monetary

values and then drawing a smooth curve through those points. As pictured,

the utility curve is concave; that is, it becomes less and less steep. The concav-

ity of the curve reflects the wildcatter’s risk aversion. To see this, consider a

simple two-outcome risk—say, a 50–50 chance of $600,000 or $200,000. By

definition, the expected utility of this risk is (.5)(100) (.5)(0) 50. Pinpoint

50 on the vertical utility scale, read over to the curve, and then read down to

the certainty equivalent value. As we saw earlier, this is $0. Now, instead of read-

ing off the curve at U 50, read over to the dashed line connecting the end-

points of the curve. Reading down, we arrive at the monetary value $200,000.

This is exactly the expected value of the risky prospect: (.5)(600) (.5)(200) 

$200 thousand. The point is that the expected value of any risky prospect always

FIGURE 12.9

The Wildcatter’s

Utility Curve

100

Utility Scale

600

70

50

25

0

–200 –120 0 200 400

Monetary Values (Thousands of Dollars)

Utility curve

Discount due

to risk

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