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December 26th, 2002

The concept of utility in economics refers to the pleasure, or relief of pain, associated with the consumption of goods and services. The terminology is derived from the utilitarian theory of social choice proposed by Bentham in the 18th century. Disregarding the difficulties of constructing a numerical measure of utility, Bentham based his utilitarian theory on the proposition that political organisations should be organised to achieve ‘the greatest good of the greatest number’ by maximising the sum of individual utilities.

Although utilitarianism, with its emphasis on rational optimisation, was compatible with the spirit of classical economics, economists made little use of utility concepts until the neoclassical ‘marginalist revolution’, associated with the names of Jevons, Menger and Walras. Their central insight was that the terms on which individuals were willing to exchange goods depended not on the total utility associated with consuming those goods, but on the utility associated with consuming the last or ‘marginal’ unit of each good. The critical point is the principle of diminishing marginal utility, based on the observation that consumption of any commodity, such as water, is first directed to essential needs, such as quenching thirst, and then to less important purposes, such as hosing down pavements.
It is the utility associated with the marginal use of the commodity that determines willingness to engage in trade at any given prices. The use of the principle of diminishing marginal utility led to a resolution of the classical ‘paradox of value’, exemplified by the observation that, wherever water is plentiful and diamonds are not, diamonds are more valuable than water, even though water is essential to life and diamonds are purely decorative.
The principle of diminishing marginal utility had egalitarian implications which Bentham almost certainly did not anticipate. If the marginal utility from consumption of an additional unit of each individual commodity is diminishing, the marginal utility from an additional unit of wealth must also be diminishing. If utility is represented as a real-valued function of wealth, diminishing marginal utility of wealth is equivalent to downward concavity of the utility function. If all utility functions are concave then, other things being equal, an additional unit of wealth yields more utility to a poor person than a rich one, and a more equal distribution of wealth will yield greater aggregate utility.
The rise of positivism and behaviorism in the early 20th Century reduced the appeal of theoretical frameworks based on the unobservable concept of utility. The ‘New Welfare Economics’ developed by Hicks (1938) and others, showed that ordinal concepts of utility, requiring only the use of statements like ‘commodity bundle A yields higher utility than commodity bundle B’ were sufficient for all the ordinary purposes of demand theory and could be used to derive a welfare theory independent of cardinal utility. An ordinal utility function allows the ranking of commodity bundles, but not comparisons of the differences between bundles.
Opponents of egalitarian income redistribution also attacked the use of cardinal utility theories to make judgements about the welfare effects of economic policies. Robbins’ (1938) claim that all interpersonal utility comparisons were ‘unscientific’ was particularly influential in promoting the idea that cardinal utility concepts should be avoided. The basic difficulty is that there is no obvious way of comparing utility scales between individuals, and, in particular, no way of showing that two people with similar income levels get the same additional utility from a given increase in income.
The apparent coup de grace was given by Samuelson’s (1947) recasting of welfare economics in terms of revealed preference. Samuelson showed that, the standard theory of consumer demand could be constructed without any overt reference to utility. Even the use of ordinal utility, Samuelson suggested, was purely a matter of expositional convenience. The analysis of consumer demand can be undertaken using only statements about preferences. Samuelson’s claim is correct in a formal sense.
However, consumers will have well-defined demand functions only if preferences over bundles of goods are convex, that is, if a bundle containing an appropriate mixture of two goods is preferred to either of two equally valued bundles each containing only one of the goods. The only plausible basis for postulating this kind of convexity of preferences is the principle of diminishing marginal utility.
Moreover, as is discussed , cardinal utility was no sooner driven out the front door of economic theory than it re-entered through the back gate of game theory and expected utility theory.

Robbins, L. (1938), ‘Interpersonal comparisons of utility: a comment’, Economic Journal 48(4), 635–41.
Samuelson, P. (1947), Foundations of Economic Analysis, Harvard University Press, Cambridge, Massachusetts.

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