If we have a utility function that translates from dollars to utility, how do we use it in making a decision? The idea of utility is that it should help us choose among alternatives with uncertain outcomes—that is, alternatives that are risky—by capturing our attitudes toward risk. If I were risk neutral and willing to make decisions based on expected monetary value, my decision trees should use expected money as the criterion for the best alternatives. Utility theory says that I should be using expected utility as the criterion in order to capture what for most of us is risk aversion.
Consider an investment decision. You have three choices: (1) a high-risk investment, (2) a low-risk investment, or (3) keeping your money in the bank without risk. If the market goes “up,” the high-risk investment returns $1500 but the low-risk investment only returns $1000. Similarly for the other uncertain outcomes shown in the decision tree below. The market can go up, down, or stay the same. The bank account is unaffected by the market. The corresponding probabilities of each outcome are shown. The expected monetary values (EMV) of the three alternatives are +$580, -$200, and $500, respectively.
DOLLAR VALUE UTILITY
$1500 1.00
1000 0.86
500 0.65
200 0.52
100 0.46
-100 0.33
-1000 0.00
The table on the right-hand side are the utility values you have assessed for yourself. What is your best alternative from an expected utility perspective? Compare this with the best alternative from EMV. Explain the difference, if any.
Sample Solution