Early Work in Economics
The turning point in Edgeworth's work was his introduction to Jevons in 1879 by a mutual friend James Sully, who in 1878 moved to Hampstead, London, where Edgeworth had lodgings in Mount Vernon and where Jevons also lived; see Sully (1918: 180, 223).
Directly stimulated by Jevons's treatment of exchange, Edgeworth became interested in the problem of the indeterminacy of the rate of exchange, arising from the existence of only a small number of traders. This led rapidly to Edgeworth's second and most important book Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (Edgeworth 1881), which was obviously written in a state of considerable enthusiasm for his new subject. Marshall's review began, ‘This book shows clear signs of genius, and is a promise of great things to come' (Marshall quoted in Whitaker 1975: 265). Jevons began by stating that ‘Whatever else readers of this book may think about it, they would probably all agree that it is a very remarkable one' (Jevons 1881: 581). However, this slim volume of 150 pages was long known only to a small group of experts, and it was not until the middle of the twentieth century that many of its central ideas began to be more fully appreciated.Part 1 of Mathematical Psychics (Edgeworth 1881: 1-15) was devoted mainly to a justification of the use of mathematics in economics where precise data are not available. There is probably no other “apology” in the whole of economic literature which compares with Edgeworth’s plea for the application of mathematics. For example, when considering individual utility maximisation:
Atoms of pleasure are not easy to distinguish and discern; more continuous than sand, more discrete than liquid; as it were nuclei of the just-perceivable, embedded in circumambient semi-consciousness. We cannot count the golden sands of life; we cannot number the “innumerable smile” of seas of love; but we seem to be capable of observing that there is here a greater, there a less, multitude of pleasure-units; mass of happiness; and that is enough (ibid.: 8—9).
Great stress was placed on comparison with Lagrange’s “Principle of Least Action” in examining the overall effects produced by the interactions among many particles. The connection with Edgeworth’s analysis of competition, involving interaction among a large number of competitors to produce a determinate rate of exchange, is central. The fact that in the natural sciences so much could be derived from a single principle was important for Jevons, but Edgeworth took this to its ultimate limit in arguing that the comparable single principle in social sciences, that of maximum utility, would produce results of comparable value. Referring to Laplace, he suggested (ibid.: 12) 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’.
Jevons’s work in the Theory of Political Economy involved the application of mathematics to the analysis of exchange in competitive markets. The crucial development following Edgeworth’s contact with Jevons was not simply the realisation that mathematics can be used to examine equilibrium in exchange. Rather, in his analysis, Jevons explicitly assumed, through his “law of indifference”, that all individuals take equilibrium prices as given and outside their control. In using this law as ‘one of the central pivots of the theory’, Jevons (1957: 87) stated that ‘there can only be one ratio of exchange of one uniform commodity at any moment’. His theory was explicitly limited to static equilibrium conditions and Jevons excluded the role of the number of competitors from his analysis via the awkward notion of the “trading body”. This followed correspondence with Fleeming Jenkin, who could not see why two isolated individuals should accept the price-taking equilibrium; see Black (1977: 166-178). However, Jevons wished to consider the behaviour of two typical individuals in a large market.
In a section on “Failure of the Laws of Exchange”, Jevons discussed cases in which some indeterminacy would result; for details of complex cases considered by Jevons, see Creedy (1992). His most notable example was house sales, where it was suggested that indeterminacy would result from the discrete nature of the good being exchanged. A reviewer suggested instead that indeterminacy ‘is really owing in our opinion to the assumed absence of competition' (Anonymous reviewer quoted in Black 1981: 157). It was this gap in Jevons's analysis which Edgeworth set out to fill. He examined how competition between buyers and sellers, through a barter process, leads to a “final settlement” which is equivalent to one in which all individuals act independently as price takers. As he later stated (Edgeworth 1925, ii: 453), ‘the existence of a uniform rate of exchange between any two commodities is perhaps not so much axiomatic as deducible from the process of competition in a perfect market'. Edgeworth's highly original analysis is discussed in the following section.
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