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Negishi on Edgeworth on Jevons’s Law of Indifference, Walras’s Equilibrium, and the Role of Large Numbers : A Critical Assessment
No full textIn developing their pure-exchange equilibrium models, Jevons (1871), Walras (1874-77), and Edgeworth (1881) make use of some version of a law, called law of indifference (or principle of uniformity) by Jevons and Edgeworth and often referred to as the law of one price in connection with Walrasian economics. Edgeworth, in particular, shares with Jevons the idea that the law of indifference must be regarded as an equilibrium property; unlike his predecessor, however, he denies the validity of the law in all economies with a finite number of traders: for him, price uniformity can only emerge and a Jevonsian or Walrasian or competitive equilibrium can only be established when the traders’ number grows unboundedly large. About one century later, Negishi (1982) resumes the time-honoured discussion about the law, striving to prove that, contrary to Edgeworth’s original conjecture, a competitive equilibrium can be attained even in small economies, provided that the true driving force underlying Jevons’s law of indifference, namely, its implicit arbitrage mechanism, be allowed to operate and carry its effects through. In this paper, after reconstructing Jevons’s, Walras’s, and Edgeworth’s respective positions, we critically discuss Negishi’s critique of Edgeworth’s stance on Jevons’s law of indifference, Walras’s equilibrium, and the role of large numbers, showing that his central claim is unsubstantiated
Hicks on Walrasian equilibrium in the 1930s and beyond
Full text linkAfter many explorations in different directions during the early 1930s, in 1934 Hicks ends up by advocating an interpretation of Walrasian equilibrium and capital theory along stationary lines, but the suggested interpretation is at variance with the view endorsed by the last Walras and by Pareto at the turn of the century. In the second half of the 1930s, during the long gestation of Value and Capital (VC), Hicks’s ideas on equilibrium and capital progressively change and mature, to eventually culminate, with the publication of VC in 1939, in the rediscovery of a method of analysis and an equilibrium concept, Hicks’s temporary equilibrium, that are substantially similar to the method of analysis and equilibrium concept put forward by the last Walras and by Pareto about forty years before. Yet this direct link with the Walrasian tradition is not overtly recognised by Hicks in VC: in particular, the essentially Walrasian character of the equilibration process supporting Hicks’s temporary equilibrium concept is carefully disguised under Marshallian garments. This fact will not only delay Hicks’s own recognition of the limits of the VC approach, which will start to be questioned by him only in the mid-1950s, but will also concur to spreading unsubstantiated ideas about the origins and theoretical foundations of the neo-Walrasian research programme. The aim of this paper is to clarify the theoretical reasons behind the winding path followed by Hicks over the 1930s, especially as far as the Walrasian conception of equilibrium and equilibration is concerned, and to identify the roots of Hicks’s ambiguity about the theoretical ancestry of the VC model in his previous intellectual histor
Hicks on Walrasian Equilibrium in the 1930s and Beyond
No full textAfter many explorations in different directions during the early 1930s, in 1934 Hicks ends up by advocating an interpretation of Walrasian equilibrium and capital theory along stationary lines, but the suggested interpretation is at variance with the views endorsed by the last Walras and Pareto at the turn of the century. In the second half of the 1930s, Hicks's ideas on equilibrium and capital progressively change. With the publication of Value and Capital in 1939, this process culminates in the rediscovery of an equilibrium concept, Hicks's temporary equilibrium, that is similar to the one adopted by Walras and Pareto about forty years before. Yet such direct link with the Walrasian tradition is not overtly recognised: on the contrary, the essentially Walrasian character of Hicks's temporary equilibrium approach is carefully disguised under Marshallian garments. The paper aims at clarifying the reasons behind the winding path followed by Hicks over the 1930s
Negishi on Edgeworth on Jevons's Law of Indifference, Walras's Equilibrium, and the Role of Large Numbers
No full textEquilibrio, disequilibrio e tempo in Walras
Full text linkWalras’s theory of general economic equilibrium goes through many changes over the twenty-six years elapsing from the publication of Walras’s first significant theoretical contribution in 1874 and the appearance, in 1900, of the fourth edition of his masterpiece, the Eléments d’économie politique pure. This paper reconstructs the main steps characterizing the twisted evolution of Walras’s ideas concerning equilibrium, disequilibrium, and time in economics. Early in his scientific career, Walras perceives, albeit confusedly, the existence of theoretical, analytical, and epistemological difficulties undermining his analysis of the tâtonnement processes associated with his equilibrium models of exchange, production, and capital formation; yet he refrains from facing such issues squarely for fear that this would compel him to give up all realistic justification in support of his theory. Concerning the exchange model, under the pressure of external criticism, Walras soon enough yields to the logical requirements of the analysis, by explicitly endorsing, since 1885, the so-called “no-trade-out-of-equilibrium” assumption, an assumption which forces him to interpret the tâtonnement process in exchange as a purely virtual equilibration process in “logical” time, supporting an “instantaneous” equilibrium notion. Concerning the production and capital formation models, however, Walras strenuously strives to preserve the pseudo-realistic assumptions permeating his original view of the tâtonnement construct: up to the third edition of the Eléments (1896), in fact, Walras keeps to the idea that the tâtonnement process in production should be viewed as an actual equilibration process in “real” time, supporting a “stationary” equilibrium notion. Yet, due to his eventual realization of the logical contradictions engendered by such interpretation of both the tâtonnement process and the associated equilibrium notion, hardly – if at all – compensated by a few dubious gains in terms of descriptive realism, in the fourth edition of the Eléments Walras eventually resolves to give up all pseudo-realistic pretence concerning the equilibration process: in 1900, in fact, he adopts a novel, openly unrealistic assumption, the so-called “hypothèse des bons”, to the effect of turning all tâtonnement processes, including those concerning production, into virtual processes in “logical” time, supporting a generalized notion of “instantaneous” equilibrium of the “temporary” type
JEL classification codes: B13, B21, B31, B41, C62, D5
Jevons, Jenkin, and Walras on demand-and-supply analysis in the theory of exchange
Full text linkIn his economic writings Jevons insists on the allegedly fundamental role played by the so-called "laws of supply and demand" in his theory of exchange; yet no demand-and-supply analysis is actually employed in deriving such theory, as developed in Chapter 4 of The Theory of Political Economy (TPE). This is all the more puzzling in the light of the following two facts: 1) in his 1868 correspondence with Jevons, Fleeming Jenkin provides a complete geometrical solution of the exchange equilibrium problem based on the use of demand and supply curves, but his suggestion is wholly neglected by Jevons in the first edition of TPE (1871); 2) in his 1874 open letter to Jevons, Walras explicitly criticizes his correspondent for his defective treatment of the "laws of supply and demand", suggesting an alternative analytical solution of the exchange problem based on the use of demand and supply functions; yet Jevons entirely disregards Walras's remarks in preparing the second edition of TPE (1879). This paper compares Jevons's, Jenkin's and Walras's approaches to the exchange equilibrium problem, explaining the analytical and epistemological reasons that underlie Jevons's neglect of his correspondents' criticism and advic
Edgeworth vs. Walras on equilibrium and disequilibrium
No full textIn a brief review of the second edition of Walras’s Eléments, published in 1889, Edgeworth criticizes Walras’s theory of tâtonnement, viewed as a misplaced and misleading attempt at explaining the equilibration process in a multi-market economy. Edgeworth’s attack sets off a controversy, raging over the 1889-1891 period, and then smouldering over the entire lives of both economists. The chief aim of this paper is to analyze the joint evolution of Edgeworth’s and Walras’s ideas on equilibrium and equilibration from the 1889-1891 controversy onwards. Even if Edgeworth’s original critique concerns Walras’s tâtonnement only, it will be proved that the fundamental divide between the two authors involves not only the dynamic, but also the static part of their respective theoretical systems. The Edgeworth-Walras controversy will be shown to produce major effects on both Walras and Edgeworth: both of them will partially revise their ideas on statics and dynamics; further, either one will take in some hints originating from the other. Yet, in spite of their reciprocal influences, their mutual communication will turn out to be quite limited. For Edgeworth will prove unable to understand the central, and unsolvable, problem of tâtonnement from Walras’s own standpoint: how to preserve a “realistic” and comprehensive picture of an observable disequilibrium process in “real” time, without disrupting the assumption of data invariance during the equilibration process. At the same time Walras will prove unable to grasp the essence of Edgeworth’s critique: that bargaining is more “fundamental” than price-taking behavior, so that the core is a broader solution concept than competitive equilibrium and recontracting a more general equilibration process than tâtonnemen
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