UNDERSTANDING SUBJECTIVE UTILITY

 

Let’s illustrate the notion of subjective utility with a simple example. Suppose you are granted the right to play the following game: you must choose between Option L and Option C, where

 • Option L ? a fair coin is tossed; you win $100 if the outcome is heads, $0 if tails
 • Option C ? you win $x for sure (certainty condition, no risk is involved)

and x is yet to be determined. The game is depicted in the following tree:

  [ut1]

Note that the expected monetary value of Option L (the lottery) is

 E(L)  =  EMV(L)  =  0.5(100) + 0.5(0)  =  $50

If you are indifferent between playing the lottery (choosing Option L) and choosing Option C given x  =  $50, we say you are risk neutral. This means that you make your decision based on the probability distribution of the lottery. You are neither risk averse nor risk preferring.

Often, however, people are willing to choose Option C even if x is lower than the expected value of the lottery, say $40. The reason for this decision-making behavior is that the lottery L involves risk (one may wind up with $0) and many people would rather avoid the risk of losing out on a sure (certain) gain of $x. People who exhibit this risk profile are said to be risk averse: they forgo the full expected value of a venture in order to minimize their exposure to risk.

There is a limit to risk aversion, though. If x were only $0.01, for instance, just about everyone would choose to play the lottery instead. In effect, the person’s decision changes somewhere as x is decreased from $50 to $0.01. Theoretically, therefore, there exists a boundary quantity x* such that the person is indifferent between playing the lottery and choosing that quantity x* with certainty. The indifference boundary may actually be a small interval (a short range of values) for some folks, in which case we would take x* to be the interval’s midpoint.

On the other hand, some people may prefer to play the lottery over a certain x = $50. This may be due to a variety of personal reasons, including a willingness to take the risk of losing out on $50 for the chance of getting $100 (the person’s favorable financial position would not be appreciably affected by a $50 opportunity loss), a pressing need for $100 (perhaps $50 simply will not do to resolve the person’s dire financial situation), or even a penchant for gambling. Whatever the reason, we say the decision maker is risk preferring.

However, as with risk aversion, there is a limit to risk preference. If x were, say $99.99, there would hardly be anyone willing to play the lottery. Once again, the person’s decision has changed and we postulate the existence of a boundary quantity x*.

In practice, x* is determined by an interview process. This is discussed on the following page.

TERMS