Philip Henry Wicksteed (1844-1927)
was an English economist who was also a Unitarian theologian (succeeding James Martineau at the Little Portland Street Chapel in London in 1874, and resigning in 1897), translator and classicist (with a particular interest in Dante) and literary critic: Wicksteed’s life is described by Herford (1931).
Turning to economics after reading Henry George’s (1879) Progress and Poverty, for many years he gave University of London Extension Lectures on economics (as part of an adult education programme). Robbins (1933: v) makes the point that “there can be few men who have so successfully combined such a wide range of intellectual pursuits with such conspicuous excellence in each of them”. The greatest influence on his economics was Jevons’s Theory of Political Economy, and he can be described, with Edgeworth, as a disciple of Jevons and a careful exponent of the subjectivist approach in which cost is interpreted in terms of foregone alternatives rather than as a “real cost”. Robbins (1931: 229) describes how Wicksteed’s copy of the second edition of Jevons’s Theory, purchased in 1882, is covered with marginal annotations.Wicksteed’s first publication in economics was his 1884 criticism of Marx, the first along Jevonian lines by a British economist, and which led to a debate with George Bernard Shaw. He published his first economics book, The Alphabet of Economic Science in 1888. This is primarily a pedagogic work expounding the utility theory of value, with a long introductory section on basic calculus. In this, he is responsible for introducing the term “marginal utility” as an improvement on Jevons’s “final utility”. This was followed in 1894 by the celebrated Essay on the Co-o rdination of the Laws of Distribution in which, in contrast to the earlier work, he states in the preface that, “I address myself only to experts”, although at the same time “without any claim to originality” (Wicksteed 1894: 3).
Although the main elements of the marginal productivity theory of distribution, according to which factors receive their marginal revenue product (marginal physical product multiplied by marginal revenue, which in a competitive goods market is equal to price or average revenue), had been proposed by a number of authors, Wicksteed is famous for his original argument that the total remuneration of all factors will precisely exhaust total revenue. Hence there is no “residual” available for distribution (in contrast to the classical approach in which rent is regarded as a residual). This led to the famous review by Alfred Flux (a Cambridge Senior Wrangler in mathematics in 1887 who, as a student of St John’s College, came into contact with Alfred Marshall). Flux made the important point that Wicksteed had implicitly assumed constant returns to scale, or linear homogeneous, production functions and, in addition, that the result is immediately given by the application of Euler’s theorem for homogeneous functions. For f (x1,..., xn) homogeneous of degree k, then Euler’s theorem states that:
Hence for k = 1 and perfectly competitive markets, the “product exhaustion” result follows. Flux (1894: 310) suggested that, “there seems no need for delaying to prove a relation so well known as this, as Mr. Wicksteed does”. It may have been “well known” to mathematicians, but Wicksteed was not a trained mathematician; indeed Herford
(1931: 200) mentions that he had been taking lessons in calculus from John Bridge, a mathematics tutor at University College London.
The assumption of linear homogeneity, along with the continuous substitutability of factors in production, was subsequently strongly criticized by Pareto, Barone and a bad- tempered Walras who unfairly accused Wicksteed of plagiarism. For further discussion of Wicksteed’s contribution, see Stigler (1941: 38-60).
Furthermore, it elicited the following comment by Edgeworth, made in his unique style: “There is a magnificence in this generalization which recalls the youth of philosophy. Justice is a perfect cube, said the ancient sage; and rational conduct is a homogeneous function, adds the modern savant”. Edgeworth’s “ancient sage” is Aristotle, who in his Nicomachean Ethics argued that justice requires equality in all directions. As a result of these attacks, Wicksteed himself became somewhat dissatisfied with his argument, though not, of course, with the main points of the marginal productivity theory.In 1910 Wicksteed published his massive Common Sense of Political Economy, described by Robbins (1931: 235) as “the most exhaustive non-mathematical exposition of the technical and philosophical complications of the so-called ‘marginal’ theory of pure economics, which has appeared in any language”. Again, Wicksteed makes no claims of originality, but this book does contain a strong criticism of the partial equilibrium analysis of supply and demand, suggesting that it does not pay adequate attention to the role of stocks of goods. He went so far as to describe the standard diagrammatic analysis as “profoundly misleading” (1910, [1933], II: 785) and actually stated that there is “no such thing” as a supply curve. He argued that although it is useful to separate the supply and demand sides of the market in considering the process of adjustment by which an equilibrium may be reached, it was of dubious value in examining the determinants of that price. He suggested that:
the cross curves of demand and supply, so often employed by economists, are really no more than two sections of the true collective curve of demand, separated out from each other, and read, for convenience, in reverse directions. These cross curves, then, as usually presented, confuse the methods by which the equilibrating price is arrived at with the conditions that determine what it is. (Wicksteed 1910 [1933] II: 797-8)
The situation he had in mind was not of firms producing only for sale but, along with other major neoclassical economists, for exchange.
He envisaged the standard exchange situation in which individuals hold stocks of a good which are brought to a market. His examples include the results of a harvest, or the “catch” of a fishing fleet (Wicksteed 1910 [1933], II: 787). Those who hold stocks also consume the good and therefore have a demand for it comparable with that of individuals who do not hold stocks. This context is thus the same as that of Jevons and Walras, Mill and Marshall (when considering international trade) and Edgeworth, yet Wicksteed took a quite independent position: See Wicksteed (1910 [1933], I: 229-34, II: 772-96, II: 797-800, II: 822-6). He referred to the conventional supply curve as a “reverse demand curve” and argued: “I say it boldly and baldly: there is no such thing... what is usually called the supply curve is in reality the demand curve of those who possess the commodity” (1910 [1933], II: 785).Wicksteed’s preferred diagram showed a curve relating the price to the total demand of possessor and non-possessors (on the horizontal axis). The equilibrium price is then obtained by the intersection of this total demand curve with a vertical line drawn from the total stock of the good available. He went on to suggest that: “a change in its initial distribution (if the collective curve is unaffected, while the component or intersecting curves change) will have no effect on the market, or equilibrating price itself, which will come out exactly the same”. (1910 [1933], II: 785-6).
However, this result was simply assumed by Wicksteed, who failed to recognize that the basic assumption, that a change in the allocation of stocks does not affect the total demand curve, requires very special conditions and generally will not hold; for details see Creedy (1991). In criticizing the partial equilibrium demand and supply analysis, Wicksteed simply replaced it with another partial equilibrium approach, instead of using the exchange context of Jevons, Walras and Edgeworth which in fact made explicit the stocks of goods held by traders in exchange.
Wicksteed’s strong rejection of the supply curve is of course associated with his “Austrian” view that all productive resources are ultimately fixed in “supply” and that cost must be seen in terms of opportunity cost; see, for example, Hutchison (1953: 104). Again, this is entirely consistent with an emphasis on exchange. As stressed by Fraser (1937: 104), the view of cost in terms of foregone alternatives is “merely the extension of the exchange relationship to the whole range of economic life”, which was of course the agenda set out by Jevons. This makes Wicksteed’s approach rather curious.
His interest in Jevons also led Wicksteed to criticize Jevons’s discussion of the famous King-Davenant law of demand, where Jevons provided a functional form which he “fitted” to the basic data which were presented by Davenant in tabular form. Wicksteed actually recognized that a third degree polynomial fits the data points exactly, and gave the parameters, adding that it “can hardly fail to stimulate curiosity as to the origin of this most interesting estimate, and the grounds on which it was formed” (1910 [1933], II: 738). He acknowledged the help of Bridge in finding the polynomial, using the “method of differences”. Yet it is interesting that neither Wicksteed nor Jevons recognized that Whewell had earlier given the precise form of the polynomial, and yet Jevons explicitly referred to Whewell; for details see Creedy (1986).
Wicksteed’s reputation stands because of his serious and extended analyses of fundamental theoretical questions. Although these analyses attracted the attention of only a small number of his contemporaries, they were without question the leaders of the economics profession. At a time when economics was becoming dominated by established academics, this was a remarkable achievement by someone who was clearly an “outsider”. More general readers are indeed likely to find his expansive style difficult to penetrate, yet it is likely that those concerned with basic questions will continue to find much interest and food for thought in his works.
John Creedy
See also:
British marginalism (II); Competition (III); Francis Ysidro Edgeworth (I); General equilibrium theory (III); Hermann Heinrich Gossen (I); William Stanley Jevons (I); Alfred Marshall (I); Vilfredo Pareto (I); Arthur Cecil Pigou (I); Value and price (III); Marie-Esprit-Leon Walras (I); Welfare economics (III).