the_development_of_utility_theory1stigler-1950-2[1]

The Development of Utility Theory. I Author(s): George J. Stigler Source: The Journal of Political Economy, Vol. 58, No. 4 (Aug., 1950), pp. 307-327 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1828885 Accessed: 01/04/2010 19:46 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Political Economy. http://www.jstor.org THE DEVELOPMENT OF UTILITY THEORY. I GEORGE J. STIGLER Columbia University But I have planted the tree of utility. I have planted it deep, and spread it wide.-BENTHAM. T HE history of economic thought can be studied with many pur- poses. One may trace the effects of contemporary economic and social conditions on economic theory or- rather more bravely-the effects of eco- nomic theories on economic and social developments. One may study the his- tory to find the original discoverers of theories, spurred on by the dream of new Cantillons; or one may compare the economics of the great economists with that of the rank and file, as a contribu- tion to the structure and process of in- tellectual change. Or one may, and most often does, simply set forth the major steps in the development of a branch of economic theory, hoping that it can be justified by its contribution to the un- derstanding of modern economics. This history of utility theory is offered pri- marily with this last purpose, although in the final section I review the history to answer the question, "Why do eco- nomists change their theories?" The scope of this study is limited in several respects. First, it covers prima- rily the period from Smith to Slutsky, that is, from I776 to I9I5. Second, the study is limited to certain important topics and to the treatment of these topics by economists of the first rank. The application of utility theory to wel- fare economics is the most important topic omitted. An estimate of the part played by utility theory in forming econ- omists' views of desirable social policy is too large a task, in the complexity of issues and volume of literature involved, to be treated incidentally. The omission is justified by the fact that most econ- omists of the period used utility theory primarily to explain economic behavior (particularly demand behavior) and only secondarily (when at all) to amend or justify economic policy.' I. THE CLASSICAL BACKGROUND ADAM SMITH Drawing upon a long line of predeces- sors, Smith gave to his immediate suc- cessors, and they uncritically accepted, the distinction between value in use and value in exchange: The word VALUE, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and some- times the power of purchasing other goods which the possession of that object conveys. The one may be called "value in use"; the other, "value in exchange." The things which have the greatest value in use have frequently little or no value in exchange; and on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce any thing; scarce any thing can be had in exchange for it. A diamond, on 1I have also omitted consideration of the crit- icisms raised by the antitheoretical writers, who played no constructive part in the development of the theory. For a discussion of some of their views see J. Viner, "The Utility Theory and Its Critics," Journal of Political Economy, XXXIII (I925), 369-87. I wish to acknowledge the helpful suggestions of Arthur F. Burns, Milton Friedman, and Paul A. Samuelson. 307 308 GEORGE J. STIGLER the contrary, has scarce any value in use; but a very great quantity of other goods may fre- quently be had in exchange for it.2 The fame of this passage rivals its am- biguity. The paradox-that value in exchange may exceed or fall short of value in use -was, strictly speaking, a meaningless statement, for Smith had no basis (i.e., no concept of marginal utility of in- come or marginal price of utility) on which he could compare such hetero- geneous quantities. On any reasonable interpretation, moreover, Smith's state- ment that value in use could be less than value in exchange was clearly a moral judgment, not shared by the possessors of diamonds. To avoid the incompara- bility of money and utility, one may in- terpret Smith to mean that the ratio of values of two commodities is not equal to the ratio of their total utilities.' On such a reading, Smith's statement de- serves neither criticism nor quotation. 2 The Wealth of Nations (New York: Modern Library, I937), p. 28. s Or, alternatively, that the ratio of the prices of two commodities is not equal to the ratio of their total utilities; but this also requires an ille- gitimate selection of units: The price of what quan- tity of diamonds is to be compared with the price of one gallon of water? Smith makes such ille- gitimate statements; for example, "The whole quantity of a cheap commodity brought to mar- ket, is commonly not only greater, but of greater value, than the whole quantity of a dear one. The whole quantity of bread annually brought to mar- ket, is not only greater, but of greater value than the whole quantity of butcher's-meat; the whole quantity of butcher's meat, than the whole quan- tity of poultry; and the whole quantity of poultry, than the whole quantity of wild fowl. There are so many more purchases for the cheap than for the dear commodity, that, not only a greater quan- tity of it, but a greater value, can commonly be disposed of" (ibid., p. 212; see also p. 838). Nevertheless, this statement can be reformulated into a meaningful and interesting hypothesis: Order commodities by the income class of consumers, using the proportion of families in the income class that purchase the commodity as the basis for choos- ing the income class. Then does aggregate value of output fall as income class rises? This passage is not Smith's title to recognition in our history of utility. His role is different: it is to show that de- mand functions, as a set of empirical re- lationships, were already an established part of economic analysis. The nega- tively sloping demand curve was already axiomatic; for example, "A competition will immediately begin among [the buyers when an abnormally small supply is available], and the market price will rise more or less above the natural price."4 The effect of income on consumption was not ignored: The proportion of the expence of house-rent to the whole expence of living, is different in the different degrees of fortune. It is perhaps highest in the highest degree, and it diminishes gradually through the inferior degrees, so as in general to be lowest in the lowest degree. The necessaries of life occasion the great expence of the poor. They find it difficult to get food, and the greater part of their little revenue is spent in getting it. The luxuries and vanities of life occasion the principal expence of the rich; and a magnificent house embellishes and sets off to the best advantage all the other luxuries and vanities which they possess. A tax upon house- rents, therefore, would in general fall heaviest upon the rich; and in this sort of inequality there would not, perhaps, be any thing very unreasonable.5 This type of demand analysis was con- tinued and improved by Smith's succes- sors, but his example should suffice to remind us that a history of utility is not a history of demand theory. BENTHAM Jeremy Bentham brought the prin- ciple of utility (to be understood much more broadly than is customary in eco- nomics) to the forefront of discussion in 4Ibid., p. 56. Substitution is illustrated by the effects of a royal death on the prices of black and colored cloth (ibid., p. 59). 5Ibid., pp. 793-94. This is of course the oppo- site of modern budgetary findings, but near-con- temporary budget studies seem to me indirectly to support Smith. UTILITY THEORY 309 England at the beginning of the nine- teenth century. In his Introduction to the Principles of Morals and Legislation (I 789) he suggested the measurement of quantities of pleasure and pain (pri- marily for the purpose of constructing a more rational system of civil and crim- inal law). Four dimensions of pleasure and pain were distinguished for the indi- vidual: (i) intensity, (2) duration, (3) certainty, and (4) propinquity.6 The first two dimensions are clearly relevant to the measurement of a pleas- ure, but the latter two are better treated as two of the factors which influence an individual's response to a particular pleasure or pain.' Bentham did not give explicit directions for calculating a given pleasure and indeed devoted a long chapter (vi) to "Circumstances Influ- encing Sensibility," which listed no less than thirty-two circumstances (such as age, sex, education, and firmness of mind) that must be taken into account in carrying out such a calculation. The theory was much elaborated with respect to economic applications in Traits de legislation (i802), a lucid synthesis of many manuscripts made by his disciple, Etienne Dumont.8 Bentham was particularly concerned with the problem of equality of income, and this 6 Op. cit., chap. iv. In addition, two further "dimensions" were added for the appraisal of the total satisfaction of an "act": the consumption of a loaf of bread might be the pleasure to which the first four dimensions refer; the theft of the loaf might be the act. These additional dimensions were fecundity and purity; respectively, the chance of one pleasure leading to another and the chance of a pleasure not being followed by a pain. 'As Bentham indicated elsewhere (see Works of Jeremy Bentham [Edinburgh: Tait, i843], I, 206; III, 214). 8 The reliability of the presentation of Bentham's views has been attested by Elie Hal6vy, La Forma- tion du radicalism philosophique (Paris: Germer Bailliere, i9oi), Vol. I, Appendix I. Here the Hil- dreth translation of the Traites is used (London: TrUbner, I87I). raised the question of comparisons of the utilities of persons who might differ in thirty-two circumstances: It is to be observed in general, that in speak- ing of the effect of a portion of wealth upon happiness, abstraction is always to be made of the particular sensibility of individuals, and of the exterior circumstances in which they may be placed. Differences of character are inscru- table; and such is the diversity of circumstances, that they are never the same for two individuals. Unless we begin by dropping these two consid- erations, it will be impossible to announce any general proposition. But though each of these propositions may prove false or inexact in a given individual case, that will furnish no argu- ment against their speculative truth and prac- tical utility. It is enough for the justification of these propositions-Ist, If they approach nearer the truth than any others which can be substi- tuted for them; 2nd, If with less inconvenience than any others they can be made the basis of legislation Thus, he achieved interpersonal com- parisons, not by calculation, but by as- sumption, justified by the desirability (somehow determined) of its corollaries. This resort to a question-begging as- sumption was a fundamental failure of his project to provide a scientific basis for social policy: the scientific basis was being justified by the policies to which it led. In one of his manuscripts he argued that this assumption was merely an abbreviation and that the con- clusions he deduced could be reached (more laboriously) without it,10 which is not in general true. Theory of Legislation, p. I03. 1O" 'Tis in vain to talk of adding quantities which after the addition will continue distinct as they were before, one man's happiness will never be another man's happiness; a gain to one man is no gain to another: you might as well pretend to add 20 apples to 20 pears, which after you had done that could not be 40 of any one thing but 20 of each just as there was before. This addibility of the happiness of different subjects, however, when considered rigorously it may appear fictitious, is a postulatum without the allowance of which all political reasoning is at a stand: nor is it more 3IO GEORGE J. STIGLER Having surmounted this obstacle no better than subsequent economists, Bentham proceeded to establish a set of propositions on the utility of in- come :11 ist. Each portion of wealth has a correspond- ing portion of happiness. 2nd. Of two individuals with unequal fortunes, he who has the most wealth has the most happiness. 3rd. The excess in happiness of the richer will not be so great as the excess of his wealth.12 Each of these propositions was elab- orated, and the utility calculus was used to defend equality ("The nearer the actual proportion approaches to equal- ity, the greater will be the total mass of happiness"), although equality was finally rejected in favor of security of property. As corollaries, gambling was utility-decreasing and insurance utility- increasing."3 fictitious than that of the equality of chances to reality, on which that whole branch of the Mathe- matics which is called the doctrine of chances is established. The fictitious form of speech (expres- sion) in both cases, which, fictitious as it is, can give birth to no false consequences or conclusions, is adopted from a necessity which induces the like expedient in so many other instances, merely for the sake of abbreviation: as it would be endless to repeat in every passage where it was used, what it was it wanted to be rigorously true" (Halhvy, op. cit., III, 48i). " Theory of Legislation, pp. 103 ff.; all state- ments italicized by Bentham. 12The use of marginal analysis was even more explicit in his Pannomicil Fragments: "But the quantity of happiness will not go on increasing in anything near the same proportion as the quantity of wealth:-ten thousand times the quantity of wealth will not bring with it ten thou- sand times the quantity of happiness. It will even be matter of doubt whether ten thousand times the wealth will in general bring with it twice the happiness. ". . . the quantity of happiness produced by a particle of wealth (each particle being of the same magnitude) will be less and less at every particle; . . ." (Works, III, 229; see also IV, 541). Theory of Legislation, pp. io6-7. In a manuscript written about I782, Bentham attempted to set forth more clearly the precise measurement of util- ity."4 We are given a definition of the unit of intensity: The degree of intensity possessed by that pleasure which is the faintest of any that can be distinguished to be pleasure, may be repre- sented by unity. Such a degree of intensity is in every day's experience: according as any pleasures are perceived to be more and more intense, they may be represented by higher and higher numbers: but there is no fixing upon any particular degree of intensity as being the highest of which a pleasure is susceptible.15 (This suggested measure will be dis- cussed in connection with the Weber- Fechner literature.) Then, shifting ground, Bentham argues that, although utility does not increase as fast as in- come, for small changes the two move proportionately,'6 so we may measure pleasures through the prices they com- mand: If then between two pleasures the one pro- duced by the possession of money, the other not, a man had as lief enjoy the one as the other, such pleasures are to be reputed equal. But the pleasure produced by the possession of money, is as the quantity of money that pro- duces it: money is therefore the measure of this pleasure. But the other pleasure is equal to this; the other pleasure therefore is as the money that produces this: therefore money is also the measure of that other pleasure.17 Unfortunately, this procedure is ille- gitimate; we cannot use an equality (or, more strictly, a constancy of the marginal utility of money) that holds for small changes to measure total utilities.'8 These suggestions are impor- 14 Lengthy extracts are given by Halvy, op. cit., Vol. I, Appendix II. "Ibid., p. 398. "lbid., p. 408. " Ibid., p. 4IO. 18 Bentham appears to have recognized this diffi- culty when, in a passage following a discussion of UTILITY THEORY 31I tant chiefly in revealing Bentham's awareness of the crucial problems in his calculus and his ingenuity in attempting to solve them.19 Bentham had indeed planted the tree of utility. No reader could overlook the concept of utility as a numerical mag- nitude; and the implications for eco- nomic analysis were not obscure. But they were overlooked. THE RICARDIANS The economists of Bentham's time did not follow the approach he had opened. One may conjecture that this failure is due to the fact that Ricardo, who gave the economics of this period much of its slant and direction, was not a Benthamite. It is true that he was the friend of Bentham and the close friend of James Mill, Bentham's leading dis- ciple. Yet there is no evidence that he was a devout utilitarian and much evi- dence that he was unphilosophical- essentially a pragmatic reformer.20 It is clear, in any event, that Ricardo did not apply the utility calculus to economics. He began his Principles with the quotation of Smith's distinc- tion between value in use and value in exchange and ended the volume with the statement: "Value in use cannot be measured by any known standard; it is diminishing marginal utility, he wrote: " [Intensity] is not susceptible of precise expression: it not being susceptible of measurement" (Codification Proposal [i822], in Works, IV, 542). '9For more general discussions of Bentham see W. C. Mitchell, "Bentham's Felicific Calculus," in The Backward Art of Spending Money (New York: McGraw-Hill Book Co., I937); and J. Viner, "Ben- tham and J. S. Mill," American Economic Review, XXXIX (I949), 360-82. 20 See Bonar's Preface to Letters of Ricardo to Malthus (Oxford: Clarendon, i887). differently estimated by different per- sons."'21 I should be content to notice that he left the theory of utility as highly developed as he found it-as much cannot be said for the theory of value-were it not for a remarkable interpretation of Marshall's: Again, in a profound, though very incom- plete, discussion of the difference between "Value