References and further reading

Baranzini, R. (2005), Leon Walras e la moneta senza velo, Torino: UTET Libreria.

Baranzini, R. (2014), ‘Pour une histoire de la theorie economique de Leon Walras’, in J.-P. Potier (ed.), Les marmites de l’histoire.

Bertrand, J. (1883), ‘Theorie des richesses: Theorie mathematique de la richesse sociale, par Leon Walras - Recherches sur les principes mathematiques de la theorie des richesses, par Augustin Cournot’, Journal des savants, September, 499-508.

Bortkiewicz, L. von (1890), ‘Leon Walras, Elements d’economie politique pure, ou Theorie de la richesse sociale. 2e edition’, Revue d’economiepolitique, 4 (1), 80-96.

Bourdeau, V. (2005), ‘L’economie politique republicaine de Leon Walras. Philosophie republicaine et economie politique en France au XIXe siecle’, doctoral thesis, UFR de Philosophie, Universite de Franche-Comte.

Bridel, P. (1996), Le chene et l’architecte: un siecle de comptes rendus bibliographiques des ‘Elements d’economie politique pure’ de Leon Walras, with R. Baranzini, Geneva: Droz.

Bridel, P. (1997), Money and General Equilibrium Theory. From Walras to Pareto (1870-1923), Cheltenham, UK and Northampton, MA, USA: Edward Elgar.

De Caro, G. (1985), Leon Walras dalla teoria monetaria alla teoria generale della produzione di merci, in L. Walras, L’economia monetaria, vol. 1, Rome: Istituto della Enciclopedia Italiana Treccani, pp. 5-200.

De Caro, G. (1988), ‘Le monde atemporel de Leon Walras’, Economies et Societes, 22 (10), 105-32.

Dockes, P. (1996), La societe nest pas un pique-nique: Leon Walras et l’economie sociale, Paris: Economica.

Dockes, P. (2011), ‘Lire Walras et les autres: une “note d’humeur”’, in R. Baranzini, A. Legris and L. Ragni

(eds), Leon Walras et l’equilibre economique general. Recherches recentes, Paris: Economica, pp.

Dumez, H. (1985), L’economiste, la science et le pouvoir: le cas de Walras, Paris: Presses Universitaires de France.

Edgeworth, F.Y (1889), ‘The mathematical theory of political economy’, Nature, 40, 434-6.

Fisher, I. (1892), ‘Mathematical investigations in the theory of value and prices’, Transactions of the Connecticut Academy, 8, 1-124.

Garegnani, P. (1990), ‘Quantity of capital’, in J. Eatwell, M. Milgate and P. Newman (eds), The New Palgrave: Capital Theory, London: Macmillan, pp. 1-78.

Jaffe, W. (ed.) (1965), Correspondence of Leon Walras and Related Papers, Amsterdam: North Holland.

Jaffe, W. (1983), William Jaffe’s Essays on Walras, D.A. Walker (ed.), Cambridge: Cambridge University Press.

Jolink, A. (1996), The Evolutionist Economics of Leon Walras, London: Routledge.

Lallement, J. (2014), ‘Walras between holism and individualism’, in R. Baranzini and F. Allisson (eds), Economics and Other Branches. In the Shade of the Oak Tree: Essays in Honour of Pascal Bridel, London: Pickering & Chatto, pp. 15-30.

Lange, O. (1942), ‘Say’s Law: a restatement and criticism’, in O. Lange et al. (eds), Studies in Mathematical Economics and Econometrics, Chicago, IL: Chicago University Press, pp. 49-68.

Maki, U. (1998), ‘Realisticness’, in J.B. Davis, D. Wade Hands and U. Maki (eds), The Handbook of Economic Methodology, Cheltenham, UK and Northampton, MA, USA: Edward Elgar, pp. 409-13.

Potier, J.-P. (1994), ‘Classification des sciences et divisions de l’“economie politique et sociale” dans Γlink between high prices in India and the UK balance of payments.

However, there is no doubt that Jevons is best remembered for his Theory of Political Economy, published in 1871. Some of the central ideas had been contained in his short “Notice of a general mathematical theory of political economy”, which was presented to the Cambridge meeting of Section F of the British Association in 1862.

Although I know pretty well the paper is perhaps worth all the others that will be read there put together, I cannot pretend to say how it will be received... I shall watch it like an artilleryman watches the flight of a shell or shot, to see whether its effects equal his intentions. (Quoted by Keynes 1936: 532)

Jevons’s article appeared in print four years later in the Statistical Journal, and is most easily found in later editions of his Theory of Political Economy.

Having failed to hit his mark, Jevons delayed producing his full-scale treatment until Fleeming Jenkin’s important paper on “The graphic representation of the laws of supply and demand” in 1870 stimulated him to publish his own work more quickly in book form, in order to establish priority. This book was not an immediate success, meeting with a negative review by Cairns and a grudging and anonymous review by Marshall. It is not clear if Jevons ever knew the identity of the author. Marshalls’ complex attitude to Jevons is discussed by Keynes (1936: 534-6). However, Jevons received support from the mathematician George Darwin, son of Charles Darwin. An anonymous piece in the Saturday Review attacked Jevons’s use of mathematics, which was said to, “wrap up a plain statement in a mysterious collection of letters” (see Black 1981: 157).

However, Jevons’s Theory of Political Economy has long been regarded as a major foundation stone of neoclassical economics. Nevertheless it is sometimes unfairly caricatured as being merely an early application of mathematics and the marginal utility analysis of demand to economics, while at the same time criticisms are directed at Jevons for not explicitly deriving demand curves from utility functions, and also illegitimately applying the theory to aggregates of a number of traders rather than single individuals.

It is therefore important to stress that Jevons’s primary emphasis was on exchange as the “central” problem in economics. Indeed, Hicks (1984) referred to the early neoclassi­cal economists as “catallactists”, in order to emphasize their exchange focus. This neolo­gism (of Whately, used also by Edgeworth) was extensively used by Hearn (1864) in his Plutology, which appears to have had some influence on Jevons, who attended a lecture by Hearn while in Australia. In the introduction to his Theory of Political Economy Jevons also praised Hearn. Hicks stressed that:

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)

Jevons and the other neoclassical writers provided a foundation for their exchange model in the form of a utility analysis and this (the ability to talk about individuals being “better off” in a particular sense) provided the basis of what came to be called welfare economics. Hicks stated that “welfare economics was captured by the catallactists and it has never got quite free” (1984: 253).

Only when the perceived central position of exchange analysis is recognized, with utility maximization as the foundation, is it possible to appreciate the enthusiasm of Jevons for his pioneering approach, nicely reflected in Edgeworth’s later remark 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... the movements of each soul, whether selfishly isolated or linked sympa­thetically, may continually be realising the maximum energy of pleasure, the Divine love of the universe. (1881: 12)

Of course, Jevons was more prosaic than Edgeworth, but Jevons’s excitement is clear in letters to his sister and brother.

Jevons’s exchange model can be described briefly as follows, using a mixture of his own and modern notation. 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 maximization, “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 as:

The term ^dy is the ratio of exchange of the two commodities at the margin. Jevons recog­nized 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).

Jevons recognized that X is equivalent to the ratio of prices of the two goods, p = p = y, but he preferred to leave p out of the equations until the equilibrium values of x and y are obtained. Recognizing 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” (1957: 101).

Jevons was subsequently criticized for describing his parties to the exchange as “trading bodies”, which appeared to consist of more than one trader on each side of the market. This seems to have been Jevons’s rather clumsy solution to a problem raised in correspondence with Fleeming Jenkin, who raised the question of indeterminacy with just two traders who were not price takers. This was before completion of the Theory of Political Economy and arose from the publication of the Jenkin’s paper on trade unions in 1868. Jenkin sent the paper to Jevons, who in reply sent a copy of his own paper which he read to the British Association in 1862. The highly revealing letters from Jenkin (in Black 1977: 166-78) devote a great deal of attention to the case of exchange between two persons. The basic difference between them was that Jevons, as explained above, explic­itly assumed price-taking behaviour, whereas Jenkin examined barter. He could not see why two isolated individuals should accept the price-taking equilibrium, writing:

There is no motive operating on their minds to induce them to agree on this rate [of exchange]. Jones would like more cotton for his silk, Brown would like more silk for his cotton and I do not see how any considerations as to the rate at which their desires fluctuate with the quantity can determine their desire for any one quantity. This must it seems to me be determined by wholly different considerations. You appear to me to assume that the ratio of exchange would be that fixed by the intersection of the curves... but in order that this should be true it would be necessary that the aggregate utilities to each party should increase up to that point which is not true. (Black 1977: 177)

As Edgeworth later made clear, in the desire to focus on price-taking behaviour for which there is a determinate solution (or solutions) to his equations of exchange, Jevons was really considering the behaviour of two typical individuals in a large market: see Edgeworth (1881: 109) who also referred to individuals “clothed with the properties of a market”. The tension arising from his model of two traders and this need for price-taking clearly led Jevons to his unfortunate term “trading body”. 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. Edgeworth’s concern was pre­cisely the role of the number of traders, and he showed that with a sufficient number of competitors the range of indeterminacy in exchange, in a barter context, shrinks to the price-taking equilibria.

Jevons clearly realized that in his model, partial equilibrium demand and supply curves are not appropriate: the diagrammatic treatment had to wait for Edgeworth’s eponymous box diagram. Nevertheless Jevons discussed the precise form of the famous King-Davenant law of demand, suggesting a functional form whose parameters he “esti­mated”, comparing his “fitted” values with the original “data”. Jevons did not realize that the “law” followed a cubic equation. See Creedy (1986) for details.

However, his further discussion of complex cases showed his confident handling of a range of subtleties. He examined situations where one dealer has very large initial stocks compared with the other trader, the extension to three traders dealing in three goods, and the case of two individuals holding stocks of one good while a third person holds stocks of the second good: these cases are examined in detail in Creedy (1992). In a section on “Failure of the Laws of Exchange”, Jevons discussed cases in which some indeterminacy would result. His most notable example was of house sales, where it was suggested that indeterminacy would result from the discrete nature of the good being exchanged. Jevons then proceeded to apply his utility analysis to other contexts. In particular he provided a treatment of labour supply, producing an elegant diagram. By extending his analysis to capital, and emphasizing the two dimensions of quantity and the time period of production, Jevons was adopted by the later “Austrian School” of economists.

These “equations of exchange” illustrate both a point of similarity and difference between Jevons and Walras (1874 [1954]), who later (with help from Paul Piccard) produced the same two simultaneous equations and, importantly, also concentrated on price-taking solutions. Despite Walras’s famous tatonnement process, 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. As explained above, Jevons left the equations expressed in terms of quantities exchanged, leaving the equilibrium price ratio to be determined by the resulting ratio of quantities. Recognizing their non-linear nature, Jevons knew that explicit solutions could not generally be obtained. Before adding a utility analysis, Walras had extended Cournot’s model of trade between two regions to produce a non-utility analysis of the exchange of two goods between two traders. He produced his general equilibrium curves in which the quantity demanded or supplied is expressed as a function of the relative price, and he had explored the form these curves might take. Hence, when faced with the equations of exchange, he realized 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 = ^pχ. Walras therefore showed how general equilibrium demand and supply functions can b^ye derived from utility functions (though he gave no explicit examples, Laundhart being the first). However, these are not partial equilibrium demand functions: for further details see Creedy (1999).

The journals and correspondence of Jevons, collected in the multi-volume edition by R.D.C. Black, clearly reveal his personal characteristics and particularly his introspec­tive nature. His own summary, made at the young age of 22 while he was in Australia and embarking on an astonishingly fertile period of self-education and discovery, pro­vides a fitting description of the man, and is worth quoting in full:

I am not so much a storehouse of goods as I am a machine for making those goods. Give me a few facts or materials, and I can work them up into a smoothly arranged and finished fabric of theory, or can turn them out in a shape which is something new. My mind is of the most regular structure, and I have such a strong disposition to classify things as is sometimes almost painful. I also think that if in anything I have a chance of acquiring the power, it is that I have some orig­inality, and can strike out new things. This consists not so much in quickness of forming new thoughts or opinions, but in seizing upon one or two of them and developing them into some­thing symmetrical. It is like a kaleidoscope; just put a bent pin in, or any little bit of rubbish, and a perfectly new and symmetrical pattern will be produced. (Quoted by Keynes 1936, p. 546) John Creedy

See also:

British marginalism (II); Capital theory (III); Competition (III); Formalization and mathematical model­ling (III); German and Austrian schools (II); Hermann Heinrich Gossen (I); Income distribution (III); Alfred Marshall (I); Carl Menger (I); Marie-Esprit-Leon Walras (I).