The term “English marginalism” generally refers to the work and outlook of a small group of economists working in England in roughly the last quarter of the nineteenth century.

These may be thought of as pioneer neoclassical economists and include, as major figures, Jevons, Marshall, Edgeworth and Wicksteed. The latter was later a strong influence on Robbins, who provided leadership for a later generation of marginalists; see O’Brien (1988).

Nevertheless, it is possible to discern differences, in views and influences, between English and continental writers during this period. Walras developed his analysis of exchange, quite independently of the English writers, as an extension of Cournot’s model of trade between regions involving a single good. Indeed, despite an extensive correspondence, his relationship with English authors cannot ultimately be described as congenial, particularly after Edgeworth’s review of the Elements where he criticised, among other things, the “exuberance of algebraic foliage”.

The Political Economy Club saw debates between Wicksteed, who produced his Jevonian critique of Marx in 1884, and the Fabian Socialist, Shaw. Earlier, around 1879, Edgeworth came into contact with Jevons, a near neighbour in Hampstead, through a mutual friend, James Sully, and their membership of the Savile Club. This led to Edgeworth’s rapid shift of attention from moral philosophy towards economics, marked by his Mathematical Psychics published in 1881.

Furthermore, the English marginalists were not always in agreement. Even though Edgeworth and Wicksteed may be described as disciples of Jevons, they were by no means slavish followers. Edgeworth (1881: 109) defended Jevons’s “trading body” in

terms of “a sort of typical couple”, but the point of departure of his work was the need to examine the role of the number of traders as an extension of Jevons’s framework, where price-taking behaviour was simply assumed. Jevons and Edgeworth also had completely different attitudes towards authority, with Jevons famously rejecting any role and Edgeworth always ready to quote an authority in support of his argument, viewing authority as almost equivalent to empirical evidence. Jevons took Edgeworth to task for the lack of transparency in his writing.

The term “English marginalism” also requires discussion. This is undoubtedly the most common description used in the secondary and textbook literature. It appears to give primacy to the emphasis on the margin or the use of calculus, so that derivatives of utility and production functions became ubiquitous (though the term “marginal utility”, replacing such awkward terms as “final degree of utility”, owes its origin to Wicksteed). It is true that Jevons, Edgeworth and Wicksteed all produced extensive apologia or justi­fications for the use of mathematics in economics and that, despite relegating his analyses to appendices, many of Marshall’s innovations were arrived at via the use of mathemat­ics and diagrammatic analyses. Nevertheless, it is worth stressing that the period marks a distinct change of emphasis, rather than simply of technique, in the study of economics. Instead of the concentration by the classical economists on the great dynamic themes of growth and development, and the important and highly sophisticated monetary debates associated with the numerous banking crises of the first half of the nineteenth century, the emphasis of the neoclassical economists was on the nature of exchange.

Exchange was seen (particularly by Jevons, Edgeworth and Wicksteed) as the “central” problem in economics. For example, Hicks (1984) referred to the early neoclassicals as “catallactists”, in order to emphasise their exchange focus.

while the classics looked at the economic system primarily from the production angle, the catallactists looked at it primarily from the side of exchange. It was possible, they found, to construct a “vision” of economic life out of the theory of exchange, as the classics had done out of the social product. It was quite a different vision. (1984: 250)

Edgeworth (1925, II: 288) summarised the position by suggesting that “in pure econom­ics there is only one fundamental theorem, but that is a very difficult one: the theory of bargain in a wide sense”. Edgeworth also stressed, “the fundamental principle of inter­national trade is that general theory which Jevons called the Theory of Exchange... which constitutes the “kernel” of most of the chief problems of economics” (1925, II: 6). He added, “distribution is the species of exchange by which produce is divided between the parties who have contributed to it” (1925, II: 13). Schumpeter (1954: 911) wrote, “they realised the central position of exchange value” which “is but a special form of a universal coefficient of transformation on the derivation of which pivots the whole logic of economic phenomena”. Furthermore, in considering the central position of exchange theory, Fraser (1937: 104) stated that the view of costs in terms of foregone alternatives is “merely the extension of the exchange relationship to the whole of economic life”.

The great success of the early marginalist or neoclassical economists was also asso­ciated with the fact that they provided a foundation for their exchange model in the form of a utility analysis. Utilitarianism was of course the dominant moral philosophy (despite lively debates during the period with idealists and social Darwinists) among the English marginalists, influenced particularly by J.S.

The success of their agenda can thus be attributed to the fact that they did indeed manage to produce a unified theory on such foundations. In looking back on the domi­nance of the “marginalists”, Hicks (1984: 252) argued:

I would therefore maintain that the principal reason for the triumph of catallactics - in its day it was quite a triumph - was nothing to do with socialism or individualism; nor did it even have much to do with the changes that were then occurring in the “real world”. The construction of a powerful economic theory, based on exchange, instead of production and distribution, had always been a possibility. The novelty in the work of the great catallactists is just that they achieved it.

It is only when the perceived central position of exchange analysis is recognised, along with the place of the principle of utility maximisation as the foundation, that it is possible to have some appreciation of the attitude behind Edgeworth’s (1881: 12) remark, after discussing the extension of utility analysis to subjects such as production and labour supply, that:

“Mecanique sociale” may one day take her place along with “Mecanique celeste”, throned each upon the double-sided height of one maximum principle, the supreme pinnacle of moral as of physical science...

Of course, other writers were much more prosaic in their expressions than Edgeworth, but his view nicely encapsulates something of the pioneering spirit of the early neoclas­sical economists.

This spirit is also displayed in Jevons’s letters to his sister and brother. Jevons, writing to his sister, suggested that, “in treating of Man or Society there must also be general principles and laws which underlie all the present discussions & partial arguments... each individual must be a creature of cause and effect” (see Black 1977: 361). His letter to his brother stated that he had, “fortunately struck out what I have no doubt is the true theory of economy, so thorough-going and consistent, that I cannot now read other books on the subject without indignation” (see Black 1977: 410). Schumpeter argued that the utility analysis must be understood in the context of exchange as the central “pivot”, and “the whole of the organism of pure economics thus finds itself unified in the light of a single principle - in a sense in which it never had before” (1954: 913). However, Marshall did not share in this enthusiasm.

The famous “equations of exchange” illustrate both a point of similarity and dif­ference between Jevons and Walras. Using similar two-person two-good exchange models, they independently produced (in Walras’s case, with help from his mathemati­cian colleague Paul Piccard) the two simultaneous equations involved, and they both concentrated on price-taking solutions. It is recognised that some commentators would dispute this point, placing much stress on different interpretations of Walras’s famous tatonnement process. However, in the formal models it is hard to escape the fact that, just as in Jevons’s approach, individuals are price-takers and in the equilibria considered, all exchange takes place at the corresponding prices. Jevons left the equations expressed in terms of quantities exchanged, leaving the equilibrium price ratio to be determined by the resulting ratio of quantities. Recognising the nonlinear nature of these equations for most forms of utility function, so that explicit solutions could not be obtained, Jevons therefore did not formally derive demand functions for the two goods in terms of relative prices. Edgeworth subsequently developed his indifference curve analysis of exchange within his box diagram and, given his emphasis on indeterminacy rather than price­taking, gave priority to the contract curve rather than demand curves.

Walras (1874) instead had previously extended Cournot’s model of trade between two regions, involving a single good, to produce a non-utility analysis of the exchange of two goods between two traders. He produced his general equilibrium demand and supply curves in which the quantity demanded or supplied is expressed as a function of the relative price. He had explored the form these curves might take, in particular, showing that in general the supply curves would be expected to be “backward bending”, essentially because suppliers also have a demand for the good of which they hold stocks. Hence, when faced with the equations of exchange, he realised that instead of trying to solve them in terms of quantities of the two goods, the concept of reciprocal supply and demand allowed him to replace one of the quantities with the product of a relative price and the other quantity, since ^y = '∖ where x and y are the amounts exchanged and p_x and p_y are the respective prices. Thi^ys reciprocal demand relationship had of course been recognised by many earlier economists, but in order to produce an exchange model, this idea needs to be combined with the idea of demand as a function of relative price. Walras is therefore credited with showing explicitly how general equilibrium demand and supply functions can be derived from utility functions: these are not the partial equilibrium demand functions which, partly through Marshall’s influence, later came to dominate economic analysis.

Formally, persons A and B hold endowments, a and b respectively, of goods X and Y. Where x and y are the amounts exchanged, utility after trade takes place can therefore be written as U_a = U_A(a - x, y) for trader A, while for B it is U_b = U_b(x, b - y): Jevons actually used additive utility functions. The “keystone” of the theory is the result that for utility maximisation, “the ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degrees of utility of the quantities of commodity available for con­sumption after the exchange is complete” (Jevons 1871, in 1957: 95, original emphasis). This gives rise to his famous “equations of exchange”, which can be expressed using modern notation as:

The term py is the ratio of exchange of the two commodities at the margin. Jevons recog­nised that the integration of these differential equations presents formidable difficulties, and for this reason he restricted his attention to price-taking equilibria, using his “law of indifference” whereby there are no trades at disequilibrium ratios of exchange and “the last increments in an act of exchange must be exchanged in the same ratio as the whole quantities exchanged” (1957: 94). This means that ⅛ can be substituted for dy in (1), giving two simultaneous equations in x and y. Jevons recognised that y is equivalent to the ratio of prices of the two goods, p = p = ⅛, but he preferred to leave p out of the equations until the equilibrium values of y and x are obtained. Recognising, as noted above, that in general the equations in (1) would be nonlinear, he did not take their formal analysis further, although he added the important but rather cryptic comment that the theory is “perfectly consistent with the laws of supply and demand; and if we had the functions of utility determined, it would be possible throw them into a form clearly expressing the equivalence of supply and demand” (Jevons 1957: 101). He showed how the equations can be used to examine some “complex cases”; see Creedy (1992).

Walras explicitly considered the step to which Jevons had merely alluded, and replaced y with px in order to suggest that the resulting equations could be solved for x and y in terms of p. He did not do this for fully specified functional forms for utility func­tions, and indeed the equations can be solved explicitly only for certain special cases. Launhardt (1885 [1993]) was later to be the first to do this, using quadratic utility func­tions. Curiously, this important step taken by Walras was not discussed by the English marginalists at all. Indeed his associated demand and supply curves seem to have been almost entirely “lost”; they do not appear in any history of economics or microeconom­ics texts. For further discussion see Creedy (1999).

They received their most extensive development by Launhardt (1885 [1993]), whose analysis was used heavily in a rather terse treatment by Wicksell (1895). The curves were discussed very briefly, in the comprehensive review of Walras’s equilibrium eco­nomics, by van Daal and Jolink (1993: 26). They commented that, “it did not get much following”, and referred to the “undeniable complexity of the figures”. The only treat­ment in general works on the history of economic analysis seems to be the terse mention by Stigler (1965: 96), who also referred to Wicksell, but not to Launhardt.

The above discussion has focused on the essential characteristics and preoccupa­tions of the British marginalists, and some differences from contemporary continental European writers. However, it is worth considering the special context in which these economists worked. Hicks is quoted above as describing the nature of the “victory” of the catallactists, but it is nevertheless true that any kind of victory from the point of view of the attitude of the profession as a whole had to wait many years.

British economics in the 1870s was going through a period of pessimism, reflected in Bagehot’s (1880: 3) comment that it “lies rather dead in the public mind. Not only... it does not excite the same interest as formerly but there is not exactly the same confidence in it”. A further symptom of the negative attitude was the attempt to exclude economics from the British Association (Section F, “Economic Science and Statistics”). There was also substantial tension between analytical economists and economic historians, such as Cunningham, and also the historical economists, such as Ingram, who were sympathetic to the German School.

The new technical innovations of the marginalists were greeted with the argument that economics was losing touch with reality. Jevons’s Theory of Political Economy was greeted with more criticism than praise, particularly regarding his use of mathematics. Marshall (in Black 1981: 146) suggested that, “the book before us would be improved if the mathematics were omitted but the diagrams retained”. Cairnes (in Black 1981: 152) argued that, “when mathematics are carried further... without constant reference to the concrete meaning of the terms for which the mathematical symbols are employed, I own I regard the practice with profound distrust”. The anonymous reviewer in the Saturday Review concluded that, “whether anything can or cannot be done in the direction indicated - and we by no means say that it cannot - Mr. Jevons has taken us a very short way” (in Black 1981: 157). Cliff Leslie wrote, “we regret that so much of Mr. Jevons’ [sic] own reasoning is put into a mathematical form, because it is one unintelligible or unat­tractive to many students of considerable intellectual power and attainments” (in Black 1981: 160).

Jevons’s reputation was indeed initially based on his applied and policy analyses. Also Edgeworth did not really establish his position until after the extensive work on index numbers, in his role as secretary to the British Association Report on Index Numbers, which produced three volumes in the late 1880s. His first professorial appointment, at King’s College London, was in 1890 when he was 45 years old. Edgeworth’s most impor­tant publication, Mathematical Psychics, was privately published in 1881 and, apart from the reviews by Marshall and Jevons, it was largely ignored for many years.

The Royal Economic Society (initially the British Economic Association - BEA) was not established, along with the Economic Journal, until 1890 and, despite Edgeworth’s editorship, the early issues contained a very broad range of studies - technical and analytical work was in a very small minority. The new journal cannot be said to have reflected a clear marginalist agenda. Indeed it was important, as Marshall stressed, to appeal to as wide a group as possible. In the same spirit no entry barriers were placed on membership of the association; for further discussion, see Coats (1968). This was not even the first economics journal in Britain: the Oxford University branch of the Christian Social Union launched its Economic Review before the Economic Journal, a move which significantly worried those who were planning to set up the BEA.

Economic debate during the period was by no means dominated by academics. Coats (1968: 370) shows that in 1891, of the 501 members of the British Economic Association who could be identified, only 86 could be described as university teachers. To this it must also be added that there were very few students of economics - even the academic econo­mists were drawn from other disciplines. The small number of economists produced by Cambridge was a regular source of complaint by Marshall, and it took him many years to establish the economics degree (the Tripos) in Cambridge.

The introduction of a marginal utility analysis of exchange also came at a time when there was much debate in Britain regarding moral philosophy. Utilitarianism may have been dominant in Cambridge, under Sidgwick, but Oxford was dominated by Idealists such as T.H. Green and F.H. Bradley who were heavily influenced by Hegel and Kant. Other approaches, such as social Darwinism, with enthusiasts such as Herbert Spencer, were also becoming popular. Thus the welfare economics and technical analysis based on utility maximisation did not initially fall on fertile ground. While it is easy from the present perspective to write in terms of a victory for English marginalists, it is neverthe­less the case that economics in England during the last quarter of the nineteenth century was carried out by a significantly heterogeneous group of writers. Furthermore, the mar- ginalists themselves did not form a unified group with a single-minded agenda. The early death of Jevons left the marginalists without a pioneering and passionate leader, and Marshall - with his much wider sympathies and broader vision - became the undisputed leader of British economics for a generation.

John Greedy

See also:

Jeremy Bentham (I); Francis Ysidro Edgeworth (I); Formalization and mathematical modelling (III); Income distribution (III); William Stanley Jevons (I); Lausanne School (II); Alfred Marshall (I); Arthur Cecil Pigou (I); Lionel Charles Robbins (I); Utilitarianism and anti-utilitarianism (III); Value and price (III); Welfare econom­ics (III); Philip Henry Wicksteed (I).