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Consumer’s Surplus

Consumer’s Surplus

BIBLIOGRAPHY

Consumer's surplus denotes the difference between the maximum amount of money a consumer would be willing to pay for a product or service and the amount he actually pays. The term was first introduced into economics by Alfred Marshall in his Principles of Economics, but the first person to enunciate the idea in a precise way appears to have been Jules Dupuit, a French engineer, in a paper published in 1844. Rudolf Auspitz and Richard Lieben (who knew of Dupuit's work but not Marshall's) gave an account of consumer's surplus in 1889 in their book Untersuchungen über die Theorie des Preises (”Investigations on the Theory of Price”); but their work was neglected, and it was Dupuit, and above all Marshall, who influenced modern economists.

The importance of consumer's surplus is that it provides a monetary measure of the benefit that a consumer derives from the supply of a product given the terms on which it is made available. It seems therefore to offer the possibility of assessing the net effect on welfare of policies that alter the terms on which different products are supplied. Economists have used the concept to argue that some systems of taxation are worse than others because they lead to a greater loss of consumer's surplus. It has also been proposed that in decreasing cost industries in which consumers' expenditures for a product would not cover total costs— if the product were sold on the market at a uniform price or, in most modern formulations, at a price equal to marginal cost—the state should make possible production of the product by means of a subsidy when the gain in consumer's surplus would justify this. In effect, what consumers would be willing to pay but do not (or, more exactly, the state's estimate of this) should be treated as an auxiliary factor in addition to what they do pay, in determining production, because it indicates as much as what they do pay the worth of the product to them.

Recent work, particularly that of J. R. Hicks, to be discussed below, not only has thrown much light on the meaning of the concept of consumer's surplus but has also revealed more clearly than before the ambiguities and complexities involved in its definition and measurement. It cannot be said that a consensus has yet emerged in the economics profession concerning the validity and usefulness of the concept of consumer's surplus.

Jules Dupuit

Dupuit was concerned with a double question: how to measure the utility derived from a public works (such as a bridge) in order to decide whether it ought to be constructed and how the charges should be set for the services it provides. Dupuit explained his general approach in his 1844 paper “On the Measurement of the Utility of Public Works.” He elaborated his views on pricing in a paper published in 1849, “On Tolls and Transport Charges.”

Dupuit argued that the amount of money paid by consumers for a product was not an accurate measure of the utility derived from its consumption. It was what a person would be willing to sacrifice to obtain a product that indicated what the product was really worth to him. More concretely, it was the maximum amount of money that a consumer would be willing to pay that measured its absolute utility or, as it has been commonly termed by later economists, its “total utility.” The difference between the maximum a consumer would pay and what he actually paid (what is now called consumer's surplus), Dupuit termed “relative utility.”

Dupuit pointed out that the absolute utility derived from any given quantity of a product would differ among consumers; and, consequently, if it were made available to all consumers at a uniform price the relative utility (consumer's surplus) for that given quantity would also differ. Furthermore, for any one consumer, the absolute utility derived from an additional quantity of the product, and consequently the maximum he would pay for it, would vary with the amount of the product that he was already consuming. Dupuit took as an example the demand for water. A fall in price would open up more uses in which the monetary value of the absolute utility of a unit of water exceeded the price, and the amount demanded would therefore expand. The difference between the sum of the maximum amounts of money a consumer would pay for the various units used for these different purposes and the amount actually spent (the price multiplied by the total number of units consumed) is his consumer's surplus.

On the basis of his analysis, Dupuit argued that in deciding whether to construct a public works it is the monetary value of the absolute utility that ought to be compared with cost. He advocated recouping this cost by a system of discriminating prices in which the price charged to different groups of consumers varied with the maximum that each group would pay (the greater the value of the absolute utility the greater the charge). It should be noted that Dupuit did not advocate a free service when marginal cost was zero. He left this question open. He pointed out that if he were to consider whether a toll should be established or not he “would have had to examine by what new tax or what increase in taxation tolls could be replaced and what would be the effects of these taxes” [seeDupuit].

Alfred Marshall. Alfred Marshall's treatment of consumer's surplus is, in essentials, similar to that of Dupuit although it shows a greater awareness of the underlying difficulties. But Marshall's practice of indicating, but at the same time glossing over, these difficulties made his exposition less clear than that of Dupuit, and there has been much discussion about what Marshall meant by his various statements, questions that probably can never be resolved beyond all doubt. Marshall's analysis seems to have been developed without knowledge of Dupuit's work. His views on consumer's surplus were first published in the privately printed Pure Theory of Domestic Values (1879) as well as in a more extended form in the first edition of his Principles of Economics (1890).

Marshall pointed out that when a consumer purchases something he is normally better off, that is, he derives a “surplus of satisfaction.” The economic measure of this surplus satisfaction is consumer's surplus, which Marshall defined as the “excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay” ([1890] 1961, vol. 1, p. 124). Marshall explained his meaning by examining the demand for tea. Suppose a consumer would just be induced to buy one pound per annum if the price were 20 shillings per pound but that if the price fell to 14 shillings per pound that he would just be induced to buy a second pound. Then, according to Marshall, the consumer would be willing to pay 34 shillings for two pounds per annum (20 shillings for the first pound plus 14 shillings for the second). But if the price were 14 shillings per pound, he would pay 28 shillings for the two pounds and thus would obtain a consumer's surplus of 6 shillings. Marshall put this argument in diagrammatic form, as had Dupuit before him (see Figure 1). If the price were OC, the quantity demanded would be OH. The maximum amount of money that the consumer would be willing to pay for the quantity OH is represented by the area OHAD. At price OC, the amount of money that the

consumer would actually pay is represented by the area OH AC. Consumer's surplus is represented by the triangular area CAD. Marshall confined his analysis to cases in which expenditure on the product represented a small part of the consumer's total expenditure. The purpose of this restriction appears to have been to ensure that the amount that a consumer would pay for additional units was not affected by the amount that he had paid for the units already demanded. Marshall's failure to deal explicitly with how he would handle the question if this restriction were removed undoubtedly contributed to a feeling that consumer's surplus was a concept of limited usefulness.

In applying his concept to actual problems, Marshall himself was suitably, and characteristically, cautious. He warned against using the loss or gain of consumer's surplus in situations in which different income groups were affected differently. He emphasized that consumer's surplus was a “rough economic measure” and suggested that the calculation should be confined to relatively small changes around the customary price, particularly when dealing with necessaries. Marshall seems originally to have had high hopes of being able to make statistical estimates of consumer's surplus, and in one case he actually made such an estimate: the loss of consumer's surplus due to the British Post Office's not allowing cheap local postal rates. But gradually Marshall became aware of the problems posed by complementarity and substitution and he became disillusioned about the possibility of making such statistical estimates, although he never revised the rather optimistic remarks included in the Principles.

Marshall illustrated the use of consumer's surplus by means of examples taken from the field of taxation. If, to refer back to the diagram, a tax of CT per unit is placed on the product and this results in a rise in price of the same amount (from OC to OT) and a reduction in the amount demanded (from OH to OM) the amount that the consumer would pay in taxes is the sum represented by the area CRBT. But the consumer is not only worse off because he has suffered a reduction in the amount available for spending represented by the area CRBT. The consumer would cease to demand the quantity MH for which he would have been willing to pay the sum of money represented by the area MHAB. He would gain the sum of money represented by the area MHAR (the money he previously spent to secure MH). The money gained would be less than the value to him of the product lost. Consequently, in addition to the loss suffered as a result of paying over a certain amount in taxes, there would be a loss of consumer's surplus represented by the area RAB. Marshall suggested that a government, having to obtain a given sum by taxation, should choose objects of taxation with a view to minimizing the loss of consumer's surplus.

Marshall's most celebrated application of the concept of consumer's surplus was his suggestion that it might be advantageous to tax industries subject to diminishing returns (in which, owing to a fall in the supply price due to the decrease in output, the loss of consumer's surplus could well be less than the proceeds of the tax) and to subsidize industries subject to increasing returns (in which, owing to the reduction in supply price brought about by the increase in output, the gain in consumer's surplus could well exceed the amount of the bounty). Thus the combination of tax and bounty might, on balance, lead to a net gain for consumers. The proposal to make price equal to marginal cost in industries in which average cost is greater than marginal cost—the amount by which consumer expenditures fall short of total costs being made up by a government subsidy (which has had the support of many modern economists)—may be regarded as a variant of the Marshallian suggestion.

Although Marshall originated the term consumer's surplus and although it did appear in the first edition of the Principles, the term that Marshall normally used until the fourth edition, in 1898, was “consumer's rent.” In view of this, it is hardly surprising to find that Marshall also introduced into economics the analogous concept of “producer's surplus,” the difference between the amount of money a producer receives for a product and the minimum for which he would be willing to supply it. It corresponds to one of the meanings of the term “rent” [seeRent]. Perhaps because the problems associated with producer's surplus are more commonly considered under the heading of rent, the separate discussion of producer's surplus has been less extensive than that of consumer's surplus. It has, however, been argued that in computing the gain from the supply of a product it is necessary to include not only the consumer's but also the producer's surplus since it is the minimum for which a producer would be willing to supply a product that represents the value of what is lost through the diversion of factors to produce it. However, a diversion of factors on any considerable scale is likely to lead to a loss of consumer's surplus elsewhere and this also needs to be taken into account. The proper although in practice extremely difficult procedure, if the additional output is to be valued including consumer's surplus, would seem to be to compare this with the value of the output lost through the diversion of the factors, including in this case the loss of consumer's surplus.

Recent developments. Marshall's analysis gained many adherents; but some economists remained unconvinced. J. S. Nicholson expressed skepticism (1894) and was answered by F. Y. Edgeworth (1894); Edwin Cannan (1924) was also skeptical and was answered by D. H. Macgregor (1924) and A. L. Bowley (1924). Doubts persisted. In recent times J. R. Hicks has attempted to rehabilitate the concept of consumer's surplus. In Value and Capital (1939), he suggested that the way to measure consumer's surplus was to discover the reduction in income that would just offset the gain brought about by a fall in price, thus leaving the consumer no better off than before. Such a definition was not subject to the Marshallian restriction that expenditure on this item be a small proportion of the total. The marginal utility of money need not be constant and it could therefore be applied to products that took an appreciable part of consumer expenditures. A. M. Henderson (1941) argued, however, that what was described by Hicks's new definition was not the Marshallian consumer's surplus, which could be regarded as the amount a consumer would pay for the opportunity of buying at the existing price the amount he was in fact buying (the alternative being to give up consuming the product entirely). Hicks's consumer's surplus was the amount a consumer would pay for the opportunity of buying at the existing price whatever quantity he wished. Since Hicks allowed the consumer to do something that according to Henderson was ruled

out by the Marshallian definition (it allowed him to adjust his consumption as the amount he had available for spending was reduced), it was to be expected that the monetary value of Hicks's consumer's surplus would, in general, be greater. Henderson also showed that the monetary value of the consumer's surplus derived from a given change in price would differ according to whether the higher or the lower price was taken as the starting point. Hicks accepted Henderson's analysis and elaborated on it in subsequent articles and in A Revision of Demand Theory (1956). Four measures of consumer's surplus were derived, depending on whether the consumer is assumed to pay to obtain or be paid to forgo the opportunity under consideration and on whether the opportunity is one in which the consumer is or is not able to adapt his consumption to take account of the payment made or received. Hicks pointed out, however, that in the cases in which Marshall made use of consumer's surplus—those in which the marginal utility of money could be assumed to remain constant—all four measures had the same value.

While Hicks's analysis clarified the problems that arise when an attempt is made to measure consumer's surplus, the formidable nature of these problems and particularly the existence of different (but equally valid) measures of consumer's surplus understandably have strengthened the tendency to regard consumer's surplus as a concept of limited usefulness. A. P. Lerner (1963) has argued that such an attitude is unwarranted, maintaining that there is no need for a consumer's surplus that assumes that the consumer is not allowed to adjust his demand to the price, a category that, according to Lerner, arose as a result of too literal a reading of Marshall. Only one consumer's surplus is needed: “the tax or the subsidy that would have the same effect on real income if it took the place of the price change considered.” He argued that consumer's surplus could help in the analysis of such problems as taxation, trade restrictions, and monopoly—the kinds of problems, in fact, for which Dupuit and Marshall devised the concept. There is no question that many economists have found the concept of consumer's surplus useful in their thinking on such questions. But until satisfactory methods have been devised to estimate in practice the gains and losses of consumer's surplus resulting from any given change in policy, other economists are likely to continue to regard the concept of consumer's surplus as, in Little's words (1950), “a theoretical toy.”

R. H. COASE

[See also the biography ofauspitz and lieben.]

BIBLIOGRAPHY

Auspitz, Rudolf; and Lieben, Richard 1889 Untersuchungen über die Theorie des Preises. Leipzig: Duncker & Humblot. -*• Published in French in 1914.

Bowley, A. L. 1924 Does Mathematical Analysis Explain? A Note on Consumer's Surplus. Economica 4:135–139.

Cannan, Edwin 1924 'Total Utility” and “Consumer's Surplus.” Economica 4:21–26.

Dupuit, Jules (1844) 1952 On the Measurement of the Utility of Public Works. International Economic Papers 2:83–110. → First published in French. DUPUIT, JULES (1844–1854) 1933 De I'utilite et de sa mesure: Merits choisis et republics par Mario de Bernardi. Turin (Italy): La Riforma Sociale.

Dupuit, Jules (1849) 1962 On Tolls and Transport Charges. International Economic Papers 11:7–31. → First published in French.

Edgeworth, F. Y. 1894 Professor J. S. Nicholson on “Consumer's Rent.” Economic Journal 4:151–158. → For further comments see pages 347–348.

Henderson, A. M. 1941 Consumer's Surplus and the Compensating Variation. Review of Economic Studies 8, no. 2:117–121.

Hicks, John R. (1939) 1946 Value and Capital: An Inquiry Into Some Fundamental Principles of Economic Theory. 2d ed. Oxford: Clarendon.

Hicks, John R. 1941 The Rehabilitation of Consumers' Surplus. Review of Economic Studies 8, no. 2:108–116.

Hicks, John R. 1943 The Four Consumer's Surpluses. Review of Economic Studies 11, no. 1:31–41.

Hicks, John R. 1946 The Generalised Theory of Consumer's Surplus. Review of Economic Studies 13, no. 2:68:74.

Hicks, John R. (1956) 1959 A Revision of Demand Theory. 2d ed. Oxford: Clarendon.

Houghton, R. W. 1958 A Note on the Early History of Consumer's Surplus. Economica New Series 25, no. 97:49–57. → An account in English of Auspitz and Lieben's views on consumer's surplus.

Knight, Frank H. 1944 Realism and Relevance in the Theory of Demand. Journal of Political Economy 52, no. 4:289–318.

Lerner, Abba P. 1963 Consumer's Surplus and Micro-Macro. Journal of Political Economy 71:76–81.

Little, Ian M. D. (1950) 1957 A Critique of Welfare Economics. 2d ed. Oxford: Clarendon. → See especially pages 166–184 on “Indivisibilities and Consumers' Surplus.”

Macgregor, D. H. 1924 Consumer's Surplus: A Reply. Economica 4:131–134.

Marshall, Alfred (1879) 1949 The Pure Theory of Foreign Trade and The Pure Theory of Domestic Values. Series of Reprints of Scarce Tracts in Economic and Political Science, No. 1. London School of Economics and Political Science.

Marshall, Alfred (1890) 1961 Principles of Economics. 2 vols., 9th ed. New York and London: Macmillan. → A variorum edition. The eighth edition is preferable for normal use.

Mishan, E. J. (1960) 1964 A Survey of Welfare Economics: 1939–1959. Pages 3–97 in E. J. Mishan, Welfare Economics: Five Introductory Essays. New York: Random House. → First published in Volume 70 of the Economic Journal. Section 4 discusses consumer's surplus.

Nicholson, Joseph S. (1893) 1902 Principles of Political Economy. Vol. 1, 2d ed. London: Black. NICHOLSON, JOSEPH S. 1894 The Measurement of Utility by Money. Economic Journal 4:342–47.

PATINKIN, DON 1963 Demand Curves and Consumer's Surplus. Pages 83–112 in Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld. Stanford Univ. Press.

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