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UTILITY AND DECISION MAKING 571

utilities for the various outcomes are assessed correctly, then the decision alternative
with the highest expected utility is the most preferred or best alternative.
Developing Utilities for Payoffs

The procedure we use to establish utility values for the payoffs requires that we first
assign a utility value to the best and worst possible payoffs in the decision situation.
Any values work as long as the utility assigned to the best payoff is greater than the
utility assigned to the worst payoff. In Swofford’s case, Table 13.9 shows that
E50 000 is the best payoff and E50 000 is the worst payoff. Suppose, then, that
we arbitrarily make the following assignments of these two payoffs:

Utility of E50 000 ¼ Uð E50 000Þ¼ 0
Utility of E50 000 ¼ UðE50 000Þ ¼ 10

Now let us see how we can determine the utility associated with every other payoff.
Consider the process of establishing the utility of a payoff of E30 000. First, we
ask Swofford’s president to state a preference between a guaranteed E30 000 payoff
and the opportunity to engage in the following lottery, or bet:

Lottery: Swofford obtains a payoff of E50 000 with probability p
and a payoff of E50 000 with probability ð1 pÞ:

If p is very close to 1, Swofford’s president would prefer the lottery to the certain payoff
of E30000 because the firm would virtually guarantee itself a payoff of E50000. On the
other hand, if p is very close to 0, the president would clearly prefer the guarantee of
E30000. In any event, as p changes continuously from 0 to 1, the preference for the
guaranteed payoff of E30000 will change at some point into a preference for the
lottery. At the change point, the president is indifferent between the guaranteed payoff
of E30000 and the lottery. For example, let us assume that when p ¼ 0.95, the
president is indifferent between the certain payoff of E30000 and the lottery. Given
this value of p,we can calculate the utility ofa E30000 payoff as follows:
UðE30 000Þ¼ pUðE50 000Þþð1 pÞUð E50 000Þ
¼ 0:95ð10Þþð0:5Þð0Þ
¼ 9:5

Obviously, if we started with a different assignment of utilities for payoffs of E50 000
and E50 000, we would end up with a different utility for E30 000. Hence, we must
conclude that the utility assigned to each payoff is not unique, but is relative to the
initial choice of utilities for the best and worst payoffs. We discuss this factor further
at the end of this section. For now, however, we continue to use a value of 10 for the
utility of E50 000 and a value of 0 for the utility of E50 000.
Before calculating the utility for the other payoffs, let us consider the significance
of assigning a utility of 9.5 to a payoff of E30 000. Clearly, when p ¼ 0.95, the
expected value of the lottery is:
EVðLotteryÞ¼ 0:95ðE50 000Þþ 0:05ð E50 000Þ
¼ E47 500 E2 500
¼ E45 000

We see that although the expected value of the lottery when p ¼ 0.95 is E45000,
Swofford’s president would just as soon take a guaranteed payoff of E30000 and thus
take a conservative, or risk-avoiding, viewpoint. That is, the president would rather
have E30000 for certain than risk anything greater than a 5 per cent chance of incurring
alossof E50000. One can view the difference between the EV of E45000 for the

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