The Utility Debate

The Utility Debate Let us first look at the term 'traditional' or 'classical' utility. The original use of the term utility was to provide an explanation of value; it was seen as a unit of pleasure or happiness that could be derived in varying degrees by consuming a commodity. The problem that early economists faced was to link this motive for obtaining commodities, with their cost. After several false starts Stigler (1950) credits the breakthrough to the eccentric German economist Heinrich Gossen: 'A person maximizes his utility when he distributes his available money among the various goods so that he obtains the same amount of satisfaction from the last unit of money (Geldatom) spent upon each commodity'. This is the first formulation of the famous marginal utility theory which may be more formally expressed as: where MU, represents the marginal utility for product 1, i.e. the satisfaction gained from consuming the last unit of that commodity, and P, represents that commodity's price. If we also add the further assumption of Jevons and Walras, that marginal utility decreases with quantity consumed, then we can derive the downward sloping demand curve (Stigler (1950)). When N-M utility was originally introduced, it was taken by some to be a means of measuring the classical utility function. The confusion was in part prompted by rather vague comments by von Neumann and Morgenstern in devising the measure (Ellsburg, 1954). Furthermore, the typical N-M curve was concave, the shape one would expect from diminishing marginal utility. As we have seen in the previous section, the concave nature of the N-M utility curve can be more plausibly explained by risk-aversion. Hence it was asserted, originally by Ellsburg (1954) and subsequently by many authors including Keeney and Raiffa (1976), that N-M utility and classical utility were quite separate concepts. However, the idea that they are totally separate seems hard to accept. For example, let us take an apparently trivial problem which nevertheless deals with the issues that we are discussing. Suppose that an N-M utility function concerning the choice of meals was drawn up. A typical question might be: Would you be indifferent between a one-course meal for certain and a 50 per cent chance of a five-course meal and a 50 per cent chance of nothing?' The respondent's attitude to risk would of course be important, but so would the satisfaction received from consumption! After all, if the person did not like the menu, it would seem reasonable for him or her to choose the single course (assuming that one of the options had to be selected and consumed), rather than risk a five-course meal. If the menu were changed to a desirable one, then the same person might choose to take the risk. The most reasonable explanation for the change in choice is the different satisfaction from con-sumption, and not a sudden conversion to a less risk-averse approach. From this and other examples that can be devised, it would seem reasonable to propose that risk attitudes are constant, and that differences in N-M utility are caused by changes in satisfaction. It is more plausible that preferences, rather than risk attitudes, change between goods. But this would imply that N-M utility contains an element of classical utility. This is exactly the proposition put forward by the concept of relative risk aversion: 'A von NeumannMorgenstern utility function confounds an individual's risk attitude with the strength of preference he feels for the outcomes' Dyer and Sarin (1982)). N-M utility is here seen as a function of two processes: first, the measuring of strength of preference for attribute levels (x) under certainty denoted by the function v(x); and, secondly, a risk function U(.) defined on the value function. Thus the utility function may be described as: U(x) = UV[V(x)] In this form, the N-M utility measure encapsulates an individual's attitude to certain consumption and his attitude towards risk. Both attitudes are normally assumed to be concave as a result of decreasing marginal utility and risk-aversion respectively (this is probably why the distinction has not been made earlier). In practice, of course, it does not seem likely that the two functions would be separated, When one is faced with a bet, for instance, the value of the prize plays an indispensable role. Relative risk-aversion in no measure disturbs the role of N-M utility in decision making. Rather, it provides an explanation of its meaning, an expla nation that provides a link between N-M utility and classical utility, as well as suggesting a reason why N-M utility curves differ over differing attributes. The development may also have measurement implications (Krzysztofowicz, 1983) though the interested reader is advised to consult French (1986, chapter 9) on such issues. Here, our interest is in the light that this development casts on our understanding of the causes of the shape of a particular N-M utility curve, as well as to show that decision making is still a developing subject.