Consumer's Surplus: Marshall and His Critics...Consumer's surplus / 27 Marshall took note of this...

Consumer's Surplus: Marshall and His CriticsAuthor(s): Peter C. DooleySource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 16, No. 1(Feb., 1983), pp. 26-38Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/134973 .

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Consumer's surplus: Marshall and his critics P E T E R C. D OO L E Y / University of Saskatchewan

Abstract. When the first edition of the Principles of Economics by Alfred Marshall was published in 1890, his theory of consumer's surplus provoked an intense controversy. Four criticisms were directly related to his original derivation of the demand curve and his analysis of consumer's surplus: first, whether an additive utility function adequately explains consumer behaviour; second, whether the marginal utility of money can be treated as a constant; third, whether the quantity demanded of one commodity can be treated as a function of its price alone; and fourth, whether it is possible make interpersonal comparisons. Marshall and his supporters responded to nearly all the critics, sometimes in articles or letters, frequently by changes in the Principles. At the end of the controversy Marshall maintained that he had not changed his position in any way.

Le surplus du consommateur: Marshall et ses critiques. Lors de la publication de la premiere edition des Principles of Economics d'Alfred Marshall en 1890, sa theorie du surplus du consommateur suscita une vive controverse. On remis en question sur quatre points sa derivation originale de la courbe de demande et son analyse du surplus du consommateur: (1) a savoir si une fonction additive d'utilite explique adequatement la conduite des consommateurs; (2) a savoir si l'utilite marginale de la monnaie peut etre trait6e comme une constante; (3) a savoir si la demande pour un bien peut etre analysee en fonction de son seul prix; et (4) a savoir s'il est possible de faire des comparaisons d'utilite entre personnes. Marshall et ses partisans re- pondirent a presque tous les critiques, quelquefois dans des articles ou dans des lettres; souvent la reaction aux critiques va se traduire par des changements dans les Principles. A la fin de la controverse, Marshall devait soutenir qu'il n'avait pas modifie son point de vue.

INTRODUCTION

When Alfred Marshall published his Principles of Economics in 1890, his doctrine of consumer's surplus and its underlying theory of consumer demand provoked an intense controversy. At worst, Marshall's critics thought his doctrine was incorrect in theory and inapplicable in practice; at best, his supporters thought his theory was only approximately true. In the third edition of his Principles, which appeared in 1895,

I wish to thank John Hicks and Paul Samuelson for their comments on an earlier draft of this paper. John Helliwell and his many helpful referees directed it toward its present form. Any remaining problems are my own.

Canadian Journal of Economics / Revue canadienne d'Economique, XVI, no. 1 February / fevrier 1983. Printed in Canada / Imprime au Canada

0008-4085 / 83 / 0000-0026 $01.50 ? 1983 Canadian Economics Association



Consumer's surplus / 27

Marshall took note of this controversy and made a number of changes in his text and in his mathematical appendices in order to answer his critics. The debate of the early 1890s was a great period of high theory; and it is important, not only because it is of historical interest, but also because it anticipated and influenced the subsequent development of economics.

Marshall was the first to derive a demand curve from utility analysis. W.S. Jevons (1871) and L6on Walras (1954a [1874-7]) had earlier shown the relation between utility and demand, but they did not demonstrate their results rigorously. Marshall's derivation is simple and direct, but it is based on a number of special assumptions. First, Marshall, like Jevons and Walras, assumed that the utility function for an individual is independent and additive, so that the utility derived from a cup of tea is independent of the quantities of coffee and sugar acquired. Second, like his predecessors, he assumed that the marginal utility derived from each commodity diminishes as additional units of that commodity are acquired. The marginal utility of money also diminishes as the purchasing power of a consumer increases; so that as a consumer with given tastes grows richer, the marginal utility of money diminishes. Third, with a given purchasing power, the marginal utility of money is constant. Thus, when a consumer allocates a given income in such a way as to maximize total utility, marginal utility divided by price is the same for each commodity and is equal to the constant marginal utility of money. The demand curve for each consumer is, then, simply the marginal utility curve for a commodity transformed by the constant marginal utility of money income. The market demand curve for a commodity represents the quantity demanded by all consumers at each price. It is necessarily downward sloping because the marginal utility of each commodity diminishes for every consumer.

Consumer's surplus did not originate with Marshall. He developed the notion from reading A.A. Cournot (1927 [1838]). J.K. Whitaker (1975, II, 240) argues that Marshall first read Cournot around 1868 and that he may have written his notes on Cournot before 1870. The influence of Cournot on Marshall's doctrine of consumer's surplus is obvious from Marshall's notes (Whitaker, 1975, ii, 242-8). Whereas Cournot measured the loss in consumer's surplus due to a per unit tax on a monopoly by the difference between the old and new prices multiplied by the new quantity purchased (Cournot, 1927 [1838], 57-62), Marshall measured it by the area between the old and new prices bounded by the demand curve. Marshall (1961, ii, 263) gave credit to J. Dupuit (1969 [1844]) for first publishing 'an exact measurement of consumers' rent,'l and he acknowledged that Fleeming Jenkin (1931 [1871]) had developed the measurement 'independently' (Marshall, 1961, ii, 533-4). Since Marshall had derived demand, an objective measure in terms of the money price, from utility, a subjective measure of well-being, he was able to demonstrate how

1 Consumer's surplus had been called consumers' rent by Marshall (1949 [1879]) in his Pure Theory of (Domestic) Values. In the fourth edition of his Principles, Marshall (1961, ii, 258) said: 'It has some analogies to a rent: but is perhaps best called simply consumer's surplus.'



28 / Peter C. Dooley

consumer's surplus relates to economic welfare.2 His demonstration, however, involved the additional assumption that it was possible to make interpersonal comparisons.

THE CRITICISMS

Marshall's Principles provoked a 'torrent of criticisms,' to quote Edgeworth (Pigou, 1966 [1925], 68), many of which dealt with consumer's surplus. Indeed, the individual comments on the doctrine of consumer's surplus, both for and against Marshall's position, were so numerous and varied (and often so repetitive) that no attempt will be made to treat them all here. Marshall (or his supporters) responded to most of the critics, sometimes in articles or letters, frequently by footnotes or other changes in the Principles. As C.P. Sanger (1924, 502), one of Marshall's students observed, Marshall 'considered all criticisms most carefully and, if he thought them well founded, made appropriate alterations in successive editions of The Principles of Economics.'

Four criticisms were directly related to Marshall's original derivation of the demand curve and his analysis of consumer's surplus: first, whether an additive utility function adequately explains consumer behaviour; second, whether the marginal utility of money can be treated as a constant; third, whether the quantity demanded of one commodity can be treated as a function of its price alone; and fourth, whether it is possible to make interpersonal comparisons. All these issues were being debated at the time Marshall's Principles first appeared.

THE UTILITY FUNCTION

Simon N. Patten (-1893a) severely criticized Marshall's doctrine of consumer's surplus in the Annals of the American Academy of Political and Social Science on the grounds that the utility derived from one commodity cannot be estimated in isolation from other commodities, because all commodities contribute jointly to the well-being of the consumer. He presented the following counter-example to Marshall's theory:

Suppose I am in a desert with three loaves of bread. To the first I might attribute 200 units of pleasure, as it would keep me alive; to the second, say 50 units, as it would make me comfortable; to the third, say five units. If instead of bread I had three pounds of meat, I might attribute to the first pound 300 units of pleasure; to the second 75 units; and to the third, say 10 units. If, as a third hypothesis, I had both articles to the amount named, could I add the two surpluses (255-385) and say I had 640 units of pleasure? Certainly not. (Patten, 1893a, 422)

In other words, if Patten had put his case in terms of the utility function, he would have insisted that Marshall use the general form.

2 Scott Gordon (1982) makes a convincing case that Marshall transposed the axes of his supply and demand curves in order to focus attention on the way real benefits and sacrifices vary with quantity, as in the case of the boy picking blackberries, instead of how consumers and producers adjust quantity to changes in price.




Patten must have hit a sore point, because Marshall responded in the next issue of the Annals with a brief note entitled 'Consumer's surplus,' saying: 'If I have interpreted him rightly, he has interpreted me wrongly' (Marshall, 1893, 619). In his defence, Marshall cited various passages in his Principles that had already dealt with the issues raised by Patten - namely, that rival commodities should be grouped together (Marshall, 1961, I, lOOn) and that utility cannot be measured at all until income is sufficient to ensure survival (Marshall, 1961, i, 841). In concluding, Marshall conceded that perhaps he could have been clearer; for he wrote: 'I will, however, confess that my account of consumer's surplus would be improved by fuller explanation, even at the expense of some repetition' (Marshall, 1893, 620).3 In the third edition of his Principles, Marshall added a new paragraph to the section immediately preceding the Giffen good, as well as a footnote citing Patten. The paragraph ended with this statement: 'we cannot say that the total utility of the two together is equal to the sum of the total utilities of each separately' (Marshall, 1961, i, 131). This, of course, implies that utilities are not independent and additive.

J. Shield Nicholson also thought Marshall was trying to measure the consumer's surplus of all things. 'Of what avail,' wrote Nicholson (1902 [1893], 58), 'is it to say that the utility of an income of ?100 a year is worth (say) ?1000 a year?' Marshall (1961, i, 127n) quoted and answered Nicholson in a new footnote to his third edition and, several years later, wrote him a letter saying: 'Some (American) writers have thought it possible to aggregate consumer's surplus for all things. I never have. If the necessaries of life be taken for granted, and a number of arbitrary assumptions made, the surplus might conceivably be elaborated. But my own attempts (made twenty-five years ago) in this direction failed so completely that I never implied it could be done' (in Nicholson, 1902 [1893], 65). The Americans were Patten, quoted above, and Irving Fisher (1965 [1892]), who considered consumer's surplus in the context of m-dimensional Euclidean space.

F.Y. Edgeworth (1967 [1881]) first proposed using a general utility function, although Marshall (1961, I, 845) thought that it was not well 'adapted to express the every-day facts of economic life.' Edgeworth's analysis was carried further by Auspitz and Lieben (1889) and by Fisher (1965 [1892]).4 Vilfredo Pareto built upon this foundation by deriving the demand relation from a general utility function, where the utility associated with any one commodity depends upon the quantities of all the other commodities acquired by the consumer. Pareto's derivation is mathematically identical to Slutsky's equation, as E. Slutsky (1952 [1915], 39n) generously acknowledged.5 Both Pareto and Slutsky published their papers in Giornale degli

3 Patten was not at all satisfied with Marshall's explanation; so he refined and repeated his criticism in the next issue of the Annals (Patten, 1893b).

4 For a detailed and scholarly discussion of the early literature on the for-m of the utility function, see 'The development of utility theory' by G.J. Stigler (1965 [1950]), who argues that Marshall's treatment of substitutes and the Giffen good required him to abandon the additive utility function. Donald A. Walker (1982) recently defended Marshall against Stigler's charge, but his defence requires the abandonment of diminishing marginal utility, for which he does not make a case. Neither Stigler nor Walker discuss Patten or Nicholson, whose criticisms tend to support Stigler's position.

5 See 'Slutsky's equation is Pareto's solution' by Peter C. Dooley (forthcoming).




economisti, one of the leading journals in economics at that time. Pareto's work also had an independent influence on the value theory of J.R. Hicks (1979, 196), who began his study of economic theory with Pareto, although Hicks did not recognize that Pareto's solution is equivalent to Slutsky's equation. Pareto proved that, when utility is jointly a function of all commodities, the demand curve need not be downward sloping. He concluded, however, that, if the cross partial derivatives are sufficiently small, a demand curve based on the assumption of an independent and additive utility function is approximately true (Pareto, 1893, 307).

Pareto's work was reviewed by Sanger (1895) in the Economic Journal, and Marshall (1961, I, 132n) cited Sanger's review in the footnote to the new section on the Giffen good, which was inserted in the third edition of Marshall's Principles. While Marshall gave credit to Sir R. Giffen for observing that the demand curve for bread could be positively sloped, no one has ever located Giffen's observation, at least not to the satisfaction of G.J. Stigler (1965 [1947], 1948). Pareto was the first to prove that a Giffen good could exist in theory; and Marshall knew about Pareto's work, if not his proof, when he was preparing his third edition.6

THE CONSTANCY ASSUMPTION

Marshall's treatment of the marginal utility of money as a constant has generated perhaps more comment than any of his special assumptions; and it has been interpreted in several different ways, both in his own time and after.

Hicks (1939, 38-41) has argued that Marshall simply 'neglected' the income effect. His interpretation runs as follows. First, if the price of a commodity (X) falls, the consumer moves to a higher indifference curve; so there is a gain in economic welfare - a gain in consumer's surplus. Second, if a compensating change is made in income (at the new price ratio) in order to put the consumer back on the original indifference curve, then for Marshall the quantity demanded of commodity (X) will be unchanged, so that the income effect will be zero for Hicks. While Hicks's interpretation may appear to be unlikely, because it implies that the quantity demanded of each commodity is the same at every level of income, it is much the same as two earlier interpretations.

Shortly after the Principles appeared, Marshall's theory of barter was politely criticized by Edgeworth (1891a) in the Giornale. Marshall (1961, ii, 792-8) wrote two letters to Edgeworth, one of which was rather angry; and he asked Arthur Berry, a Cambridge mathematician, for some assistance. Berry responded to Edgeworth with a letter (in Marshall, 1961, ii, 793-5) and with an article in Giornale (Berry, 1891).

6 Several years later, when Edgeworth (1925, in, 166) criticized the notion of the Giffen good, Marshall (Pigou, 1925, 441) responded with the example of a man travelling between two points in Holland. Suppose he does not have enough money to make the whole journey by railway (the superior good) and must travel part of the distance by canal boat (the inferior good). If the boat fare rises, he must reduce the distance travelled by railway and increase the distance travelled by canal, which is the Giffen paradox. A mathematically identical illustration appears in Pareto's Cours (1896-7, II, 338-40), which Marshall had read.

7 For a discussion of these letters and the related articles in Giornale, see the note by C.W. Guillebaud (Marshall, 1961, ii, 791-8).




In his response Berry used a peculiar utility function8 first employed by Edgeworth (189 1a), himself, where the marginal utility of one commodity (X) diminishes at the same time as the marginal utility of the other commodity (Y) is constant. Under these conditions, if commodity (Y) is money, its marginal utility is constant; and all indifference curves have the same slope at any given quantity of commodity (X). The income-consumption curve is, therefore, parallel to the Y-axis; and the income effect would be zero, as Hicks argued. Marshall (1961, i, 844-5) cited this argument with approval in a new Note xii bis to his mathematical appendix. This line of reasoning is rather messy, however, because it contradicts Marshall's original assumption that the marginal utility of money diminishes as income increases, and it creates an unnecessary adding-up problem - namely, as income increases at given prices, the quantity demanded of every commodity remains unchanged.

Edgeworth (1891b) accepted much of Berry's argument and apologized for having misinterpreted Marshall. A few years later, when Nicholson (1902 [1893], 1894) criticized the constancy assumption, Edgeworth (1894a, 1894b) came to Marshall's defence, although this little skirmish did not lead to a decisive victory.9 Enrico Barone (1894b) picked up where Edgeworth left off. According to Barone's interpretation of the constancy assumption, a fall in the price of commodity (X) will change the purchasing power of the consumer and, in most cases, change the quantities of the other commodities (Y) demanded. If, however, a compensating change is made in income to hold the marginal utility of money constant, then the quantities demanded of the other commodities (Y) will remain unchanged. Since the quantity of commodity (X) is supposed to remain the same before and after Barone's compensation, the income effect is zero; and Barone has much the same interpetation of Berry and Hicks. Marshall (1961, i, 132n) cited Edgeworth and Barone in his defence against the attack of Nicholson.

Milton Friedman (1953 [1949]) interprets Marshall's demand curve as being derived along a single indifference curve. While a fall in price will move the consumer to a higher indifference curve, a compensating variation in income should be made to keep the consumer on the original indifference curve in order to derive the Marshallian demand curve. This interpretation is rather nice in many ways: It requires the demand curve to be downward sloping; it keeps the marginal utility of money constant; it allows consumer's surplus to be measured by the change in real income, and it does not lead to the counter-factual and theoretically impossible result that all Engel curves are vertical. If Marshall had been allowed to choose between the interpretations of Hicks and Friedman, he may well have preferred Friedman's, but he was not given the choice. He endorsed Berry's rebuttal of Edgeworth and Barone's defence against Nicholson, which implies that he accepted Hicks's interpretation. '0

8 The peculiar utility function used by Edgeworth (1891a, 237n) is U = D1 (x) + ay, where a is a constant. The indifference curve is, then, dyldx = -41'(x)/a, so that, when x is given, the slope of the indifference curve is constant.

9 The bright spot in this exchange was Edgeworth's (1894b, 155n) reference to Dr A. Voigt, who had suggested that utility could be measured by 'only ordinal - not cardinal - numbers.'

10 Friedman intended his interpretation to apply to Marshall's original theory of demand, as it appeared in the first edition of the Principles. In the third edition, Friedman argues, Marshall made a number of changes that are inconsistent with his original theory, for example, the Giffen good.




Paul A. Samuelson (1966 [1942]) treats Marshall's special assumptions strictly in terms of their mathematical implications. He demonstrates that 'the combined assumptions of constancy of the marginal utility of income and independence of utility imply that the elasticity of demand always be unity (Samuelson, 1966 [1942], 82).' He also shows that the incomne elasticity of demand is unitary, so that every commodity would be the same percentage of the consumer's budget at every level of income. For Samuelson, these conclusions are counter-factual; therefore, he rejected Marshall's theory.

Samuelson's conclusions were not entirely new. Many years earlier Pareto and Barone had explored the relation between the constancy assumption and price elasticity, though not income elasticity. Pareto showed that if the utility derived from one commodity is independent of the quantities of the other commodities possessed, a constant marginal utility of money income implies that the price elasticity of demand for all commodities is constant (Pareto, 1892b, 494) and equal to unity (Pareto, 1892a, 225). He also proved that these were only sufficient conditions and that it was also necessary to specify that the number of commodities does not change (Pareto, 1892b, 494). For Pareto, like Samuelson, these conditions were counter-factual; therefore, he rejected the assumption that the marginal utility of money could in general be treated as a constant, but he conceded that it would be approximately true for a minor commodity like nutmeg. Barone (1894a, 434-6) added that the marginal utility of money will be constant, when the price of one commodity changes, if the elasticity of the marginal utility curve for that commodity is unity. Pareto's results were included in Sanger's (1895) review, which was footnoted by Marshall (1961, I,

132n); so Marshall must have been aware of this line of criticism. As a matter of theoretical purity, Marshall recognized that the marginal utility of

money income could not be treated as a constant. He referred his critics to the change that he had made in his mathematical appendix, Note VI, in which he took formal account 'of changes in the marginal utility of money (Marshall, 1961, i, 132n).' As a matter of practical application, however, he argued that it was legitimate to neglect 'the second order of small quantities (Marshall, 1961, I, 132n).' On this point he received strong support from Edgeworth (1894b, 347-8), who wrote 'the assumption that the marginal utility of money is constant, is (1) theoretically correct, being analogous to the received methods of physics; and (2) practically useful;' from Barone (1894b), who quoted both Marshall and Edgeworth; and from Fisher (1965 [1892], 31), who said: 'This is nearly true when only one commodity is considered.' Edgeworth, Barone and Fisher all worked from the analogy of physics."

THE DEMAND FUNCTION

Walras's main criticism of the theory of consumer's surplus was directed against the assumptions of partial equilibrium analysis. It was aimed equally at the works of Cournot, Dupuit, Auspitz and Lieben, and Marshall, as he explained in a letter to 11 Alan Abouchar (1982) recently criticised this conventional conclusion, although he does not treat

the historical controversy: Edgeworth, Berry, Nicholson, Pareto, Barone, Fisher, or Sanger.




Maffeo Pantaleoni (Jaff6, 1965, letter 913). In his comment on Auspitz and Lieben, Walras (1954b [1890], 484) stated:

The quantity sold of any product is a function not only of its own selling price, but also of the selling prices of all other products and the prices of all productive services. Messrs. Auspitz and Lieben assume that the selling prices of other products and the prices of all productive services can be held constant, while the selling price of the product under consideration varies. Theoretically, they have no right to do this. The selling prices of products and the prices of productive services are mutually interrelated.

Walras (1954b [1890], 486) concluded that 'the definite integral of the demand function does not represent total utility' and does not measure consumer's surplus. Marshall must have considered and rejected Walras's criticism, perhaps for several reasons.

Most importantly, Marshall intended his economic theory to be an approximate description of reality that could be applied in practice; whereas Walras stressed conceptual clarity and logical rigour. Partial equilibrium analysis was essential to Marshall's purpose; general equilibrium to Walras's. For Marshall (1961, i, 773): 'The function then of analysis and deduction in economics is not to forge a few long chains of reasoning, but to forge rightly many short chains and single connecting links.' As he wrote to Walras in 1889, 'the right place for mathematics in a treatise on Economics is the back-ground' (Jaffe, 1965, letter 922). Earlier he had written: 'I cannot be said to have accepted Mr. Jevons doctrine of "final utility". For I had taught it publically in lectures at Cambridge before his book appeared. I had indeed used another name vis: "terminal value-in-use". But following the lead of Cournot I had anticipated all the central points of Jevons book, and had in many respects gone beyond him. I was in no hurry to publish because I wished to work out my doctrines on their practical side' (Jaff6, 1965, letter 595). The 'practical side' of Marshall's economics is perhaps best illustrated by his measurement of elasticity. And it was on operational grounds that he defended his assumptions of independent utilities and the constancy of the marginal utility of money income, 'for there are very few practical problems, in which the corrections to be made under this head would be of any importance' (Marshall, 1961, I, 132).

To a certain extent Walras's dismissal of consumer's surplus was undercut by Barone (1 894b), who showed that a consumer's surplus for one individual in isolation could be determined within a Walrasian system and that it could be reconciled with Marshall's treatment. In order to handle Walras's criticism that a change in the price of one consumer good affects the quantities of productive services offered by a consumer, Barone divided consumer optimization into two parts: selling productive services and buying consumer goods. Suppose a consumer sells productive services and receives money; having received money, the consumer buys products. If selling and buying occur at the same set of prices, Marshall and Walras have identical solutions. A gain in consumer's surplus can arise for both of them, if income is received at one set of prices and consumer goods are purchased at another (lower) set; Walras would arrive at a different measure of consumer's surplus than Marshall,




however, because Marshall holds the marginal utility of money constant, whereas Walras does not. For Walras, the quantities demanded of all goods change when one price changes; for Marshall, the price and quantity of only one good changes. Barone showed that the two measures differ by a small amount. If a compensating change in income is made in Marshall's case, so that his consumer can buy the same quantities of all the other goods at constant prices, then the consumer's surpluses of Marshall and Walras are equal. They are approximately the same if 'the second order of small quantities,' to use Marshall's phrase, is neglected. 12

The distinction Barone makes between the Marshallian and Walrasian measurements of consumer's surplus is much the same as the difference between the Marshallian and compensated variation measurements of consumer's surplus made many years later by Hicks (1939) and extended by A. Henderson (1941). 13 Marshall seems to have been interested only in the demonstration that the two measures differ by a small amount, which may or may not be true. 14

Barone's gain in consumer's surplus arises from a sort of 'false trading' - trading at disequilibrium prices for the individual consumer. Income is received under one set of prices, while expenditures are made under another set of prices. If the price of one consumer good falls after income has been received, the gain in economic welfare is a windfall. Clearly, all consumers cannot enjoy windfalls simultaneously, so that interpersonal comparisons are needed to demonstrate a gain in welfare for society.

INTERPERSONAL COMPARISONS

Patten (1893a, 1893b), Nicholson (1902 [1893], 1894), and Fisher (1965 [1892]), among others, criticized Marshall for making interpersonal comparisons of utility. They argued that it was not possible to compare the satisfaction that two different people derive from their expenditures. Marshall was well aware of this criticism long before his Principles appeared. In 1879 he made the following qualification to the measurement of consumer's surplus in The Pure Theory of (Domestic) Values: 'allowance must be made for the fact that a satisfaction which a rich man values at a shilling is slight in comparison with the one for which a poor man will be willing to pay a shilling' (Marshall, 1949 [1879], 22).

In the Principles, Marshall considered making interpersonal comparisons under three different circumstances. First, in order to extend the notion of consumer's surplus from a single person to people in general, Marshall (1961, I, 130) said, 'it would naturally be assumed that a shilling's worth of gratification to one Englishman

12 Walras (Jaff6, 1965, letters 1188, 1190) indicated to Barone that he still did not accept Marshall's theory of demand - or supply, for that matter; and Barone (Jaff6, 1965, letter 1191) agreed that Marshall's theory was only approximately correct, whereas Walras's was the exact solution. Walras's criticism that a change in the price of one consumer good will affect the quantity of factor services supplied by a consumer also applies to Slutsky and Hicks.

13 Hicks (1981) has recently published a corrected and simplified version of his contributions to this subject under the old title of 'The four consumer's surpluses' in his collected essays, Wealth and Welfare.

14 See J.A. Hausman (1981).




might be taken as equivalent with a shilling's worth to another, "to start with," and "until cause to the contrary were shown."' In other words, consumer's surplus would be a true measure of economic welfare if every person had the same utility function and the same income.

Second, consumer's surplus is an approximate measure of a gain or loss in economic welfare, because 'it happens that by far the greater number of events with which economics deals, affect in about equal proportions all the different classes of society' (Marshall, 1961, I, 131). This apparently means that all consumers have the same utility functions, as before, and that incomes, while not equal, are not redistributed by most economic events. These are, to be sure, rough and ready conditions.

Finally, when Marshall came to apply his doctrine of consumer's surplus, he acknowledged that in a limited sense, 'it is true that a position of equilibrium of demand and supply is a position of maximum satisfaction' (Marshall, 1961, i, 471). How, then, can economic welfare be improved, if it is already at a maximum? How can there be a gain in consumer's surplus? Here Marshall had to come to grips with the Walrasian problem of general equilibrium. He discussed three cases where economic welfare might be improved: (1) when income is redistributed from the rich to the poor, (2) when a commodity is produced under conditions of increasing returns, and (3) when multiple positions of (stable) equilibrium exist.

Income redistribution increases economic welfare under Marshall's supposition that all people - or, at any rate, all Englishmen - enjoy the same amount of satisfaction when they have the same income. When incomes are unequal, the poor gain more than the rich lose as incomes become more equal. In the case of industries subject to increasing returns, Marshall argued that a situation might exist where a bounty would induce firms to increase production and reduce price, so that consumers would enjoy a gain in economic welfare. If the gain to consumers exceeds the bounty to producers, then society would enjoy a net gain in economic welfare. 'And if a general agreement could be obtained among consumers, terms might be arranged which would make such action amply remunerative to the producers, at the same time that they left a large balance of advantage to the consumers' (Marshall, 1961, i, 472). This is the compensation principle, and it does not require interpersonal comparisons of utility. Thus, Marshall recognized that interpersonal comparisons could be made in terms of money without reference to utility, although he did not pursue the idea.15 Unfortunately, this particular case rests upon the validity of Marshall's law of increasing returns, which he attributed to improvements in industrial organization. Such improvements are not consistent with static competitive equilibrium. If the original position of equilibrium is unique, a bounty cannot improve it. If it is not unique, we have the case of multiple positions of equilibrium, which Marshall (1961, I, 472n) said were 'not of great practical importance.'

15 For further discussion of the compensation principle, see N. Kaldor (1969 [1939]) and Hicks (1981 [1939], 1981 [1941]) as well as the criticisms of T. de Scitovsky (1969 [1941]), who shows that the principle may lead to ambiguous results, owing to the index number problem.




CONCLUSION

Marshall did not change his theory of consumer demand in the third edition of his Principles. 'Truth,' he wrote several years later to J.B. Clark, 'is the only thing worth having: not peace. I have never compromised on any doctrine of any kind' (Pigou, 1966 [1925], 418). Judging 'truth' in historical perspective, gives the advantage to Marshall's critics. The general utility function has replaced the independent and additive form. Marginal utility has nearly disappeared, not to mention its constancy for money. Demand is generally treated as a function of all prices and income. And Marshall's interpersonal comparisons of utility have given way to Pareto's optimum. The reason Marshall kept to his original theory has been well-expressed by J.M. Keynes (1933, 275) in comparing Edgeworth with Marshall: 'Edgeworth wished to establish theorems of intellectual and aesthetic interest, Marshall to establish maxims of practical and moral importance.' Marshall thought that pure theory would not help to improve the lot of mankind as immediately and directly as his own maxims.

Marshall's victory over his critics is a curiosity and may have more to do with the sociology of economics than the force of logic. Marshall's Principles became the standard textbook on economics. His authority was so great that debate ceased and progress stopped. His critics were no longer read; so the next generation of eonomists (Hicks, Samuelson, and others) had to rediscover independently much of the work that had been done, though not completed, nearly fifty years earlier.

REFERENCES

Abouchar, Alan (1982) 'Marshall, consumer surplus, and the marginal utility of money.' Eastern Economic Journal 8, 79-82

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