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Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis

Léon Walras, Irving Fisher et l’approche de la Cowles Commission à l’analyse de l’équilibre général
Robert W. Dimand
p. 253-280

Résumés

Cet article s’intéresse à la relation entre le travail de Walras et une tradition particulièrement influente de l’équilibre général, à savoir celle associée avec la Cowles Commission for Research in Economics (située au Colorado dans les années 1930s et à l’université de Chicago de 1939 à 1955) et la Cowles Fundation, successeur de la Cowles Commission, établie à l’université de Yale à partir de 1955. Irving Fisher a introduit aux Etats Unis l’analyse en équilibre général, dans sa thèse de doctorat Mathematical Investigations in the Theory of Value and Prices, soutenue à Yale en 1891 (publiée en 1892) ; on doit à Fisher également la première traduction en anglais d’une monographie de Walras. Fisher n’avait pu accéder à des exemplaires des ouvrages de Walras et Edgeworth que lorsque sa thèse de doctorat était presque terminée ; il découvre à ce moment qu’il vient de réinventer, indépendamment, l’approche en équilibre général déjà développée par d’autres ; cependant, Fisher ira plus loin que Walras, en construisant des mécanismes hydrauliques pour simuler le calcul d’un équilibre général, et il sera en avance sur Pareto, en utilisant des courbes d’indifférence. Dans les années 1930, Fisher était en étroite collaboration avec Alfred Cowles, à la Cowles Commission, à l’Econometric Society et Econometrica, actif dans la promotion des méthodes formelles, mathématiques et statistiques, en économie, en contribuant à attirer l’attention sur les contributions de Walras, Edgeworth et Pareto. A la Cowles Commission, le premier travail de recherche substantiel et systématique sur l’équilibre général, appliqué au commerce international, avait été réalisé par Theodore Yntema, directeur de la recherche à la Cowles Commission de 1939 à 1942 et auteur de A Mathematical Reformulation of the General Theory of International Trade (1932) et par l’étudiant de Yntema, Jacob Mosak, auteur de General Equilibrium Theory of International Trade (1944). Un corpus de travaux postérieurs, bien plus connu, sur l’existence de l’équilibre général, a été développé à la Cowles par Kenneth Arrow et Gerard Debreu (travaillant au départ indépendamment, mais aboutissant à une co-publication majeure) et par Lionel McKenzie, tous les trois chercheurs associés à la Cowles Commission à Chicago au début des années 1950. Après le déménagement de la Cowles à Yale, le moteur de la recherche sur l’équilibre général à la Cowles Foundation a été Herbert Scarf et son travail sur le calcul de l’équilibre général (que Scarf reliait aux premières tentatives de Fisher, par exemple en présentant son approche dans sa contribution à Ten Economic Studies in the Tradition of Irving Fisher, 1967). Fisher et puis la Cowles Commission ont donc constitué le canal par lequel l’équilibre général atteignit les sciences économiques en Amérique du Nord. Cet article fait partie d’une histoire plus large de la Cowles Commission et de la Cowles Foundation, commissionné par la Cowles Foundation.

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  • 1 The Cowles Commission became a foundation when Alfred Cowles 3rd provided an endowment in place of (...)

1General equilibrium analysis reached the Western Hemisphere in Irving Fisher’s 1891 Yale doctoral dissertation (published as Fisher, 1892) and developed in Colorado and Chicago at the Cowles Commission for Research in Economics (an institution in whose founding Fisher, the founding president of the Econometric Society, was closely involved) and then at its successor from 1955, the Cowles Foundation at Yale.1 Fisher’s shock at discovering that his invention of general equilibrium analysis had been preceded by Walras led to the translation of Walras (1892) and the 1892 election of Walras as an honorary foreign member of the American Economic Association. The Cowles Commission and Foundation was the setting for the famous work of Kenneth Arrow and Gerard Debreu (1954) and Lionel McKenzie (1954a) on proving the existence of general equilibrium (McKenzie’s work was as firmly rooted in the Cowles Commission research program as that of Arrow and Debreu). Cowles subsequently was the setting for Herbert Scarf (1967; 1973) on computation of equilibria (and other important work in general equilibrium, e.g. Truman Bewley, 2007), but also for Martin Shubik’s game-theoretic critique of the classical general equilibrium as “incomplete and not adequate” for analysis of a monetary economy (Shubik, 1975; 1999-2010) and for now less-remembered general equilibrium reformulations of international trade theory (Jacob Mosak, 1944; cf. Theodore Yntema, 1932). Walras’s writings, like those of Cournot, first reached anglophone readers in translations by Fisher’s brother-in-law Nathaniel Bacon, supervised and introduced by Fisher (Cournot, [1838] 1897; Walras, 1892), and interest in Cournot, Walras, Pareto and other pioneers in mathematical economics was stimulated by public lectures by Fisher and others at the Cowles summer research conferences in Colorado Springs in the 1930s, notably by Harold Davis and René Roy marking the Cournot centenary in 1938 (which Fisher, 1938 celebrated in Econometrica), and, in the earliest years of Econometrica, by articles on early mathematical economists (Jevons; Marshall; Hicks, 1934 on Walras; Schneider, 1934 on von Thünen). At a time of renewed interest at Cowles and Yale in Fisher’s economics (Fellner et al., 1967), Scarf (1967) emphasized that his work on computable general equilibria was in the spirit, and revived the tradition, of the hydraulic model of general equilibrium in Fisher’s dissertation (see also Brainard and Scarf, 2005). In contrast to this direct link with Fisher (1892), Fisher’s contribution to the Arrow-Debreu-McKenzie developments was the indirect one of promoting the Cowles Commission as a uniquely supportive space for mathematical economics at a time when such research was far from mainstream within the economics profession and when political upheavals had disrupted European foci of mathematical economics such as Karl Menger’s Vienna colloquium (some of whose leading members, such as Wald, came to Cowles).

1. Irving Fisher: Equilibrium, Indifference Curves and a Hydraulic Model

  • 2 After receiving his PhD in 1891, Fisher was an assistant professor of mathematics at Yale for three (...)
  • 3 Samuelson made that statement in 1967 in a volume in honor of Fisher, where praise of Fisher was to (...)

2Irving Fisher earned Yale’s first PhD in political economy (jointly with mathematics)2 with a thesis that Paul Samuelson modestly acclaimed as “the greatest dissertation in economics”3 (in Fellner et al., 1967, 22) although Robert Dorfman (1995, 23n) held that “If Fisher’s examiners had been better versed in European economic literature than they were, a promising career might have been blighted at its inception.” As a Yale undergraduate and graduate student Fisher studied engineering and mathematics with the mathematical physicist Josiah Willard Gibbs. But he also took political economy courses with William Graham Sumner, the professor of political and social science, because the charismatic Sumner, a Social Darwinist and pioneering sociologist, was a campus celebrity. When Fisher had completed his coursework, he was stumped for a thesis topic that would span both his fields of interest and could be supervised jointly by Gibbs and Sumner. Sumner told Fisher that he had heard of something called mathematical economics and, while he did not claim to know much about it, could direct Fisher to books by W. Stanley Jevons (1871) and by Rudolf Auspitz and Richard Lieben (1889). Visitors to the Centre Walras-Pareto at the University of Lausanne are shown Walras’s copy of the 1879 second edition of Jevons’s Theory of Political Economy ([1871] 1970). Next to Jevons’s statement that in principle all prices and quantities should be determined simultaneously but that this would be too difficult mathematically is Walras’s marginal comment, “C’est fait, mon garçon.” Challenged by Jevons’s remark but unaware of Walras, Fisher proceeded to invent general equilibrium analysis for himself.

3A few weeks before the submission of his completed thesis in 1891, Fisher finally managed to obtain copies of books by Walras (1874-1877) and Francisco Ysidro Edgeworth (1881), having found the titles of their books in Harriet Jevons’s expansion of Jevons’s bibliography of mathematical economics in an 1888 posthumous edition of Jevons’s Theory. Fisher was shocked to discover that general equilibrium analysis, the system of equations describing the simultaneous determination of all prices and quantities, had already been invented by Walras and Edgeworth. Fisher had gone beyond Walras’s and Jevons’s cardinally measurable utility by introducing ordinal utility, indifference curves and marginal rates of substitution (before Pareto), but so had Edgeworth. Fisher had gone beyond both Walras and Edgeworth in considering the conditions for the utility function be integrable: if the gradient of utility “is not distributed in the above manner integration is impossible and there is no such quantity as total utility or gain” (Fisher, 1892, 88-89, Fisher’s emphasis). But this advance, while noteworthy, was not comparable to the invention of general equilibrium analysis and had been anticipated by Giovanni Batista Antonelli (1886), which was not translated into English until 1971. Following Harriet Jevons’s bibliography of mathematical economics, Antonelli (1886) appeared in Fisher’s bibliography, but Fisher, who could read French and German, stated that “In the case of Italian and Danish writings, with which I am wholly unacquainted and in the case of a large number of others which I have not been able to see or examine, I have been guided by book notices or the wording of the title” (Fisher, 1892, 120).

  • 4 Distance and publication in obscure local journals were not the only barriers to communication: Alb (...)

4Such surprises were more common when books and journal articles crossed the ocean by ship4 and did not mean that Yale was then a scientific backwater (at least, not Gibbs’s laboratory). According to Bill Bryson (2003, 116-117; 121), “In 1891 [Max Planck] produced his results and learned to his dismay that the important work on entropy had in fact been done already, in this instance by a retiring scholar at Yale University named J. Willard Gibbs.” Gibbs’s On the Equilibrium of Heterogenous Substances

“has been called ‘the Principia of thermodynamics,’ but for reasons that defy speculation Gibbs chose to publish these landmark observations [as a series of articles from 1875 to 1878] in the Transactions of the Connecticut Academy of Arts and Sciences, a journal that managed to be obscure even in Connecticut, why is why Planck did not hear of him until too late … From 1902 to 1904 [Albert Einstein] produced a series of papers on statistical mechanics only to discover that the quietly productive J. Willard Gibbs in Connecticut had done the work as well, in his Elementary Principles of Statistical Mechanics of 1901.”

5Notice that Gibbs wrote about equilibrium, that he was a scientist capable of preempting Planck and Einstein, and that his mentor’s example explains why Fisher (1892) chose to publish his dissertation in the Transactions of the Connecticut Academy of Arts and Sciences.

  • 5 The machine is no longer extant and perhaps was lost when Fisher’s financial reverses forced him to (...)

6Even after allowing Walras’s priority for general equilibrium and that of Edgeworth for ordinal utility and indifference curves, and apart from his discussion of integrability, Fisher (1892) achieved a major advance. He not only considered how to find the equilibrium prices and quantities but, as befitted a Gibbs student, he constructed a hydraulic mechanism to simulate the determination of equilibrium prices and quantities, represented by the equilibrium depths and volumes of water in the various compartments of Fisher’s model (see Brainard and Scarf, 2005; Dimand and Ben-El-Mechaiekh, 2012; and the photograph of Fisher’s 1893 mechanism in Fisher, 1997, Vol. 1, 41). Fisher’s hydraulic mechanism was unfortunately destroyed in transit to be exhibited at the Columbian Exhibition, held in Chicago in 1893 (a year late for the 400th anniversary of Columbus’s landing), but Fisher eventually built another in 19255 (see photograph in Fisher, 1997, Vol. 1, 42). Appropriately, Herbert Scarf (1967) announced his algorithm for computation of general economic equilibria in a contribution to Ten Economic Studies in the Tradition of Irving Fisher. Not only was Fisher (1892) a striking contribution to general equilibrium analysis, with the first attempt at computable general equilibrium, but, beyond economics, it was a landmark in the history of computing before electronic computers. One can only wonder what a slightly earlier Yale PhD (in philosophy), Thorstein Veblen, also co-supervised by William Graham Sumner, must have thought of the idea of building a physical analogue of the economy to see what the equilibrium prices and quantities would be. But from the standpoint of mathematical economics and general equilibrium analysis, Vilfredo Pareto wrote to Fisher from Lausanne in 1897, “Ce sont précisément les jeunes économistes, comme vous, qui feront faire les progrès nécessaires à l’économie politique et qui la feront devenir une vraie science. J’espère avoir fait un 1er pas, mais vous et d’autres vous ferez d’autres pas bien plus grands!” (Pareto, 1958, Pareto’s emphasis).

7Fisher moved on to the study of intertemporal equilibrium in The Rate of Interest (1907), introducing the “Fisher diagram” for the terms of trade between current consumption and future consumption (1907, 409). Samuelson argued that “the greatest contribution in Fisher’s 1907 classic is its presentation of a definitive model of general equilibrium determination of interest rates … this completely anticipates in its formal structure the post-1930 models of international trade that Haberler, Viner, Lerner, Leontief, Meade and others developed; and the 1907 Fisher system, which antedates the work of Slutsky (1915) or W. E. Johnson’s classic exposition of indifference curves (Economic Journal, 1913), is completely isomorphic to the microeconomic model of general equilibrium in J. R. Hicks, Value and Capital (1939)” (Samuelson in Fellner et al., 1967, 30, italics in original; see also Dimand, 2019a, Chapter 4).

8The shock of encountering Walras (1874-1877) and Edgeworth (1881) made Fisher determined to pay, and draw, attention to his predecessors in mathematical economics, and to avoid intellectual isolation from advances in economics in Europe. Part I of Walras’s “Geometrical Theory of the Determination of Prices” (1892) was translated under Fisher’s supervision and published with an introductory note by Fisher in the Annals of the American Academy of Political and Social Science, while Parts II and III were still forthcoming in French. The unnamed translator was presumably Nathaniel T. Bacon, Fisher’s wife’s brother-in-law, who went on to translate Cournot ([1838] 1897) with a substantial introduction and notes by Fisher, and with a bibliography of mathematical economics (173-210) greatly extending Appendix IV of Fisher (1892, “Bibliography of Mathematico-Economic Writings,” 120-124), which in turn extended the bibliography of W. Stanley Jevons and Harriet Jevons. Appendix III of Fisher (1892, 106-119) examined “The Utility and History of Mathematical Method in Economics,” with extensive quotations from the works that Fisher should have read before writing his thesis. Fisher’s introduction to the translation of Cournot was the basis for “Cournot and Mathematical Economics” (Fisher, 1898). Walras was elected an honorary foreign member of the American Economic Association in 1892, presumably at Fisher’s initiative. Fisher spent 1893-94 meeting almost every prominent European economist outside Scandinavia, visiting Walras and Pareto in Lausanne, Edgeworth in Oxford, Marshall in Cambridge, Barone in Florence, Pantaleoni in Rome, and Menger, Böhm-Bawerk, Wieser and Lieben (but not Auspitz) in Vienna, and attending mathematics and physics lectures by Frobenius and Helmholtz in Berlin (where the lectures of historical economists such as Schmoller disappointed Fisher).

  • 6 Except for Zawadzki (1914) and the French translations of Fisher and of Auspitz and Lieben, these b (...)
  • 7 “Cette étude est dédiée à I. FISHER auquel la théorie de capital, du revenu et du taux de l’intérêt (...)
  • 8 A referee notes that Fisher’s dissertation was mentioned by Allais in 1943 in an earlier book, A la (...)

9Fisher’s dissertation was translated into French by Jacques Moret as Fisher (1917), as part of a brief outpouring of books of commentary on and exposition of mathematical economics published in French in Paris and Lausanne, outside the French university system, by French, Swiss, Portuguese and Polish admirers of Walras and Pareto: Leseine and Suret (1911), Boven (1912), Osorio (1913), Étienne Antonelli (1914), Zawadzki (1914), Moret (1915) and Suret’s 1914 translation of Auspitz and Lieben6 (see Zylberberg, 1990). But although Maurice Allais dedicated his magnum opus, Économie et Intérêt (1947), to Irving Fisher7 and cited Moret (1915) and wrote the 1947 Revue d’économie politique memorial article on Fisher, the five books by Fisher cited in Allais (1947) did not include Fisher’s dissertation on general equilibrium8 and the dedication invoked only other contributions of Fisher. There is no evidence that Allais introduced Fisher (1892; 1917) to his student Gerard Debreu or that Debreu discovered it for himself, since he never cited it (see, e.g., Debreu, 1959 or Debreu, 1983, a collection of twenty of his articles). All the Fisher citations in Allais (1947) were to French translations of Fisher’s books on capital and interest and on the purchasing power of money. Thus, although Charles F. Roos and Harold T. Davis, the two research directors of the Cowles Commission in Colorado Springs in the 1930s, were both strong admirers of Fisher (1892), and although Debreu studied with Fisher’s admirer Allais, Fisher had only an indirect influence on general equilibrium analysis at the Cowles Commission in Chicago in the 1950s through his role in fostering the Commission as a space for mathematical economic theory in an era when such research was far from mainstream in the economics discipline, rather than any direct influence through any knowledge at that time of his dissertation by Arrow, Debreu or McKenzie. Later, however, at a time of renewed interest in Fisher at the Cowles Foundation at Yale (Fellner et al., 1967), Herbert Scarf (1967) emphasized the relevance of the hydraulic mechanism in Fisher (1892) to his own work on computable general equilibrium (see also Brainard and Scarf, 2005).

2. The Early Years of the Cowles Commission

  • 9 The society had less than twenty-two dollars in assets when Cowles became treasurer in April 1932.

10The Wall Street crash of October 1929, in addition to marking the onset of the Great Depression, ruined the reputation and personal finances of Irving Fisher, who notoriously had declared that stock prices appeared to have reached a permanently high plateau. Starting from nothing, Fisher had accumulated in the stock market boom of the 1920s a fortune of ten million dollars, of which he then lost eleven million, a substantial sum of money even for an economics professor as John Kenneth Galbraith remarked (Fisher, 1997, Vol. 13; Dimand, 2019a, chapters 7 and 8). Fisher’s net worth was negative until his sister-in-law died in 1945, forgiving the million-dollar debt in her will. But the stock crash also created an opportunity for Fisher’s mathematical economics, econometrics and general equilibrium analysis to shape the development of the economics profession. The crash disillusioned an avid producer and consumer of stock forecasts, Alfred Cowles 3rd, a grandson of one of the founders of the Chicago Tribune. Cowles turned to mathematical statistics to demonstrate that stock forecasts were worthless and that stock forecasters had done no better than chance (see Dimand and Veloce, 2010; Dimand, 2019a, chapter 9). Cowles, who lived in Colorado Springs, turned for advice to Harold Davis, an Indiana University mathematics professor and Colorado College graduate who summered in Colorado Springs. Davis told Cowles about the Econometric Society, founded at the very end of 1930. To create a forum for his results, and because his research led him to appreciate the work of other econometricians, Cowles wrote in August 1931 to Irving Fisher, founding president of the new (and impoverished9) Econometric Society, offering to pay for a research institute and a scholarly journal, starting with $12,000 a year. Others in the Econometric Society understandably viewed such an unsolicited offer of major funding in the depths of the Great Depression in 1931 as a crank letter, but Cowles was a Yale graduate (class of 1913) and had been in the Yale senior society Skull and Bones, and his father and uncle had been in Skull and Bones with Fisher when the three were Yale undergraduates in the 1880s (so the Cambridge Apostles are not the only student society with a place in the history of economics). Cowles thus became president of the Cowles Commission for Research in Economics (with Fisher on an advisory council), treasurer of the Econometric Society (and from 1937 also secretary), and business manager of Econometrica.

11In addition to its permanent research staff and monographs, the Cowles Commission held month-long summer research conferences in econometrics and mathematical economics in Colorado Springs annually from 1936 through 1940, with an entire morning or afternoon for each paper. Thus, on Friday, July 12, 1940, Wassily Leontief reported in the morning on “Some Results of an Empirical Study of the General Equilibrium” (based on his forthcoming book on input-output analysis, Leontief, 1941), Paul Samuelson in the afternoon on “The Stability of Equilibrium” (Samuelson, 1941-1942), at the close of a week that also featured Abraham Wald on a new foundation for maximum likelihood and W. Edwards Deming on sampling. The following Wednesday, July 17, was devoted to Irving Fisher on the velocity of circulation of money and Trygve Haavelmo on “The Problem of Testing Economic Theories by Means of Passive Observations.” Paul Samuelson, then a graduate student, later recalled ruefully that the usual excellent wines were missing from dinners at Cowles’s home when Fisher, a fervent teetotaler and prohibitionist, attended (Dimand, 2019a, chapter 9). In contrast to the Cowles Commission summer conferences, the meetings of the Econometric Society, the other venue for advanced research in econometrics and mathematical economics, lasted only three days, with more than one three-paper session at a time and half an hour for presentation and discussion of each paper.

12In addition to serving on the advisory council, Irving Fisher was a regular participant in the Cowles conferences, for example opening the July 1936 conference with four days of lectures on “Income in Theory and Income Taxation in Practice” (Fisher, 1937) but did not speak at Cowles about general equilibrium or revisit the themes of his dissertation.

  • 10 Wald’s proof was less general than those of Arrow and Debreu and of McKenzie “since Wald assumes fi (...)
  • 11 The RAND Corporation translated the two Wald papers as part of its research on linear programming a (...)
  • 12 Arrow, in Arrow et al. (1991, 12), mentioned that Menger, then teaching mathematics at the Illinois (...)
  • 13 Although Triffin taught at Yale for two decades after the Cowles Foundation moved there in 1955, hi (...)

13Abraham Wald, a full-time research fellow at the Cowles Commission from July 1938 and continuing as a Cowles research consultant after his move to Columbia University as Harold Hotelling’s assistant, had pioneered proofs of the existence of general equilibrium in a stationary economy10 in two papers at Karl Menger’s mathematics colloquium in Vienna (Wald, [1934] 1968; [1935] 1968, translated in Baumol and Goldfeld, 196811, expounded less formally for a wider audience in Wald, [1936] 1951, and examined by Düppe and Weintraub, 2014, 2016). Articles by Hans Neisser ([1932] 1990), Karl Schlesinger, Heinrich Stackelberg and Frederik Zeuthen in 1932 and 1933 had shown that counting equations and unknowns to show existence of an equilibrium, as Walras, Marshall and Cassel had done, was inadequate to demonstrate existence of a meaningful equilibrium with non-negative quantities (see references and discussion in Arrow and Debreu, 1954). A third Wald paper, which was to have derived demand functions from individual utility maximization and which may have given a fixed-point proof of existence of general competitive equilibrium, was announced as forthcoming in the next volume of Menger’s Ergebnisse but the Menger colloquium disappeared along with Austrian independence in 1938 and the paper has been lost (Düppe and Weintraub, 2016, who report Arrow’s hunch that Wald was likely to have seen the generalization of his earlier work). Wald’s talks at the 1938, 1939 and 1940 Cowles summer conferences and at the 1945 Cowles conference on the econometrics of dynamic economic models were on mathematical statistics rather than general equilibrium. Wald’s contributions to postwar Cowles conferences and monographs on econometric method, after his move to Columbia’s Department of Statistics, also concerned statistical theory, not economic theory. The mathematician Karl Menger (son of the economist Carl Menger) spoke at the 1937 Cowles conference after emigrating from Vienna to the United States, but his talk on “An Exact Theory of Social Relations and Groups” had more affinity to Pareto’s sociological writings than to his economics and did not touch on general equilibrium analysis or the Vienna colloquium.12 Apart from Samuelson on stability of equilibrium and Leontief’s input-output empirical application at the 1940 conference, Walrasian general equilibrium analysis appeared in the 1939 Cowles conference when Samuelson’s fellow Harvard graduate student Robert Triffin spoke about “Monopoly in Particular-Equilibrium and in General-Equilibrium Economics,” citing his forthcoming dissertation on Monopolistic Competition and General Equilibrium Theory (1940).13

  • 14 Lionel McKenzie recalled that “I was present [as a Princeton graduate student between 1939 and 1941 (...)
  • 15 The first of von Neumann’s 1928 minimax papers (1928a, much less known than the longer article late (...)
  • 16 Nor, judging from the papers they wrote at the time, in New York where Marschak and Neisser were co (...)
  • 17 Arrow (in Arrow et al., 1991, 10-11), in a paper given in June 1983 on the 50th anniversary of the (...)

14In addition to Wald and Menger, another participant could have linked the Cowles Commission to the general equilibrium theorizing of the Menger colloquium: Jacob Marschak. Marschak, then the founding director of Oxford’s Institute of Statistics, spoke at the 1937 and 1939 Cowles conferences. He became research director of the Cowles Commission at the beginning of 1943 (serving as director until 1948 and as a member of Cowles until 1960) and would have taken that position in 1938 had the Cowles Commission’s grant application to the Rockefeller Foundation been successful (see Dimand and Hagemann, 2020a; 2020b). In Axel and Earlene Leijonhufvud’s oral history project on emigré economists, Marschak recalled lecturing the role of mathematics in economics to Leo Szilard’s informal mathematics study group in Berlin around 1928 (Weintraub, 1983, 13n; 1985, 74n; Marchionatti, 2019, 1390). Marschak spoke about the general equilibrium equations for a stationary economy, presumably a draft of the manuscript published in translation after his second emigration as Marschak (1934), on which see Dimand and Hagemann (2020a). “One of the mathematicians became extremely agitated and began a stream of interruptions, arguing that the equilibrium relationship should be described by inequalities instead of equations. The mathematician was von Neumann” (Weintraub, 1985, 74n). Marschak’s presentation thus provided the initial stimulus for John von Neumann’s paper on existence of equilibrium for a growing economy (von Neumann, [1937] 1945), presented in Princeton in 193214 and published in 1937 in the proceedings of Menger’s colloquium. Marschak’s recollection showed that, although it was not published until 1937, von Neumann’s paper on existence of general equilibrium originated in the same time and place as his two 1928 articles on a fixed-point proof of the existence of a minimax solution to two person zero-sum games15. As Weintraub (1985, 74n) remarks, “The min-max idea, the duality ideas, and the strategy of proof to be used later for the fixed-point theorem are found in each paper.” But Wald, Marschak and Menger did not follow up at the Cowles Commission and the Cowles conferences16 the general equilibrium discussions in which they had participated in Berlin and Vienna. Kenneth Arrow, who took Hotelling’s and Wald’s course in mathematical statistics, recalled that he did not learn of Wald’s Ergebnisse papers from Wald but probably from Hotelling (Weintraub, 1985, 96).17

  • 18 Neither Yntema (1932) nor Mosak (1944) cited Fisher (1892). Both referred primarily to Edgeworth, P (...)

15Where general equilibrium analysis did figure prominently in the early years of the Cowles Commission was in international trade theory. International trade was a context that often turned the thoughts of economists to general equilibrium considerations. As Kenneth Arrow remarked, “[John Stuart] Mill’s own theory of reciprocal demand is a true general equilibrium theory of international trade” unlike Mill’s Ricardian theory of domestic values (Arrow in Kehoe et al., 2005, 15). Alfred Cowles moved to Chicago to take over his family’s investments when his father died in 1939, and the Cowles Commission left Colorado to become affiliated with the University of Chicago, filling the gap left by the death of Henry Schultz, who had spoken at the 1938 Cowles conference about “Mathematics in Economics” and “Statistics in Economics” (see Schultz, 1938; Lange et al., 1942). The international trade theorist Jacob Viner joined the Cowles Commission advisory council to represent the university’s Economics Department, and his younger colleague Theodore Otte Yntema, a statistics professor in what was then the university’s School of Commerce and Administration (now the Graduate School of Business), became research director of the Commission (from 1939 to the end of 1942). Yntema’s 1929 Chicago PhD dissertation, supervised by Viner and Schultz, was published as A Mathematical Reformulation of the General Theory of International Trade (1932). Viner, Yntema and Oskar Lange supervised Jacob Mosak’s 1941 Chicago doctoral dissertation, published as General-Equilibrium Theory in International Trade (Cowles Commission Monograph No. 7, 1944)18. Although Mosak began his dissertation after Schultz’s death, his preface emphasized that Schultz had first introduced him to “the mathematical school of economists” (see also Mosak, 1942, in the volume in Schultz’s memory). As Mosak (1944, 33-35) pointed out, his formulation of general equilibrium in international trade dropped some simplifications made by Yntema: Yntema assumed the existence of supply and demand function while Mosak (under Yntema’s supervision) derived them from utility and transformation or production functions, Mosak wrote demands as functions of all prices where Yntema made demand for each commodity a function of that commodity’s price deflated by the general price level.

16Taken together, Yntema (1932) and Mosak (1944) marked an advance in the formal, mathematical, general-equilibrium formulation of international trade theory, and Arrow and Hahn (1971, 12) credited Mosak (1944) along with a slightly later paper by Lloyd Metzler with initiating “the current trend in comparative statics and stability,” yet they have been almost entirely overshadowed in the literature of trade theory (see e.g. the well-known surveys of trade theory by Gottfried Haberler, Jagdish Bhagwati and John Chipman in the 1950s and 1960s reprinted in Dimand, ed., 2004, Vol. 10, or the essays on the history of Cowles in Arrow et al. 1991, where Mosak 1944 got one sentence from Debreu on p. 28, reporting only that it originated as a dissertation). Mosak (1944) was reviewed on its appearance in a survey of “Recent contributions to general equilibrium analysis” by Hicks (1945) and cited in the second edition of Value and Capital (Hicks, [1939] 1946, 7 n1, 257 n2), as well as by McKenzie in the introduction to a conference volume on the fiftieth anniversary of Value and Capital (McKenzie and Zamagni, eds., 1991, xx, xxix). Like Roos and Davis, Yntema and Mosak barely appeared in the history of the Cowles Commission as presented by, for example, Arrow, Debreu, Malinvaud and Solow (1991). Partly this is because journal articles now have more impact in economics than books (especially if each article makes a single, memorable point), and partly because the authors did not remain academics: Mosak spent his career with the United Nations, and Yntema, after moving from Cowles to the policy-oriented Committee for Economic Development in 1942, joined the Ford Motor Company in 1949 as a vice-president for finance, rising to be chairman of the finance committee (what would now be termed chief financial officer, CFO). But there was also a fortuitous element of timing, also relevant to Mosak’s decision not to pursue an academic career. Mosak was clearly one of the two outstanding economics undergraduates of his year at the University of Chicago—but he was inevitably in the shadow of his classmate Paul Samuelson. Rather than follow up his dissertation with further contributions to trade theory and equilibrium analysis, which would have helped retain the profession’s attention for his thesis, Mosak chose not to compete and instead had a long, distinguished non-academic, non-publishing career.

3. Arrow-Debreu-McKenzie: Existence and Stability of General Equilibrium

  • 19 The Cowles Commission became the leading center of general equilibrium research just as the Univers (...)

17Lionel McKenzie (1954a) and, in a joint paper after initially working independently (see Arrow, 1951b; Debreu, 1951; 1952a; 1952b; 1954; Düppe, 2012), Kenneth Arrow and Gerard Debreu (1954) used Shizuo Kakutani’s fixed-point theorem (Kakutani, 1941) to prove existence of general equilibrium with considerably greater simplicity and generality than Abraham Wald had done nearly twenty years before. As Arrow and Hahn (1971, 10) remarked, “Wald’s papers [translated in Baumol and Goldfeld, 1968] were of forbidding mathematical depth, not only in the use of sophisticated tools, but also in the complexity of the argument. As they gradually came to be known among mathematical economists, they probably served as much to inhibit further research by their difficulty as to stimulate it.” Like Wald before them, Arrow, Debreu and McKenzie all had Cowles Commission connections. Arrow spent two years at the Cowles Commission at the University of Chicago, writing his Cowles Monograph on Social Choice and Individual Values (1951a), famed for the “Arrow impossibility theorem” showing that no social welfare function can satisfy a specific set of plausible-sounding axioms. He continued to be listed as a research consultant to the Cowles Commission long after moving to Stanford University. Debreu spent eleven years with the Cowles Commission and Foundation in both Chicago and New Haven. McKenzie spent a year beginning with the fall semester of 1950 at the Cowles Commission as a special graduate student visiting the University of Chicago, attending the graduate courses and seminars of Tjalling Koopmans (on activity analysis) and Jacob Marschak, before returning to teaching at Duke University, his undergraduate alma mater, for the fall semester of 1951 and was listed as a Research Consultant in the Cowles Foundation’s reports for 1956-1958, 1958-1961 and 1961-1964. He reprinted McKenzie (1954b) in a Cowles Commission Paper, presented a seminar at the Cowles Foundation at Yale in 1956, authored two Cowles Foundation Discussion Papers in 1956 (unrelated to his seminar paper), and reprinted two of his articles as Cowles Foundation Papers in 1957 (one of them a revision of one of the previous year’s discussion papers)19. Both McKenzie (1954a) and Arrow and Debreu (1954) were presented to the Econometric Society in Chicago, December 27-29, 1952, and McKenzie’s paper, which was submitted first by at least two months, was published in the issue of Econometrica preceding the one with Arrow and Debreu’s article (despite refereeing delays—John Nash never submitted his report), yet a Google Scholar search by Roy Weintraub (2011, 211) found some 2,300 citations of Arrow and Debreu (1954) and only 197 citations of McKenzie (1954a). Even Weintraub (1979, 27n, italics in original), when urging that the term Arrow-Debreu model of general equilibrium be replaced by Arrow-Debreu-McKenzie, did so on the grounds that “the proof of existence on which current work is based came out of McKenzie (1959),” without any mention of McKenzie (1954a) or any of McKenzie’s pre-1959 articles. Although, as Weintraub and Gayer (2001) discovered, a referee (a mathematics professor, not an economist) had recommended rejection of Arrow and Debreu (1954), that article figured prominently (together, in Arrow’s case, with Arrow, 1951a) in the citations for their Nobel Memorial Prizes.

  • 20 In 2009, McKenzie wrote to Roy Weintraub (2011, 209) that “Actually I did visit the Cowles Commissi (...)

18McKenzie’s work on general equilibrium emerged from his involvement in international trade theory and from his time at the Cowles Commission20, although McKenzie (1954a; 1954b; 1955a; 1955b) were all written after his return from Cowles to Duke in the fall of 1951 (and were published well before he finally received his PhD from Princeton in 1957). McKenzie (1954b), showing that bilateral comparison of comparative advantage was insufficient to find the efficient allocation of world production, originated in work done in Tjalling Koopmans’s Chicago course on activity analysis (Koopmans, 1951, cited in all four of McKenzie’s 1954 and 1955 papers; see also Koopmans, 1957, Essay I) and was based Frank Graham’s trade theory, which McKenzie had encountered as a pre-World War II doctoral student at Princeton (McKenzie, quoted by Weintraub, 2011, 200-201; see also Graham, 1948; Whitin, 1953; McKenzie, 1955a; McKenzie, 2002; Düppe and Weintraub, 2014). McKenzie (1954a) was dedicated “to the memory of my friend and teacher, Frank D. Graham.” A suggestion by Koopmans (research director of Cowles 1948-1955 and 1961-1967) to examine Samuelson’s factor-price equalization theorem in the context of activity analysis led to McKenzie (1955b). In the second footnote of McKenzie (1954b) he expressed his “wish to thank Professor Tjalling C. Koopmans for his encouragement and support. The debt to my old teacher, Frank D. Graham, will be apparent.” McKenzie’s articles in 1954-55 stemmed both from his time studying activity analysis with Koopmans at the Cowles Commission in 1950-51 and from his earlier study of international trade theory with Graham. Although McKenzie’s existence proof applied much more generally than just to Graham’s trade model, indeed as generally as Arrow and Debreu (1954), its appearance in a series of articles in international trade theory starting from Graham’s model may have contributed to McKenzie (1954a) receiving less attention than Arrow and Debreu (1954) because its title and McKenzie’s other 1954 and 1955 articles led economists to think of McKenzie (1954a) as a contribution just to the international trade literature.

  • 21 Weintraub (2011, 213, n13) reports that “Nikaido had independently developed a proof of existence o (...)

19Both Arrow and Debreu (1954) and McKenzie (1954a) provided existence proofs for general equilibrium simpler and more general than that of Wald nearly two decades before, as did Nikaido (1956)21. There were some differences between the two papers, but these were of secondary importance. Arrow and Debreu started from Nash’s proof of existence of a solution for n-person games (Nash, 1950), assumed consumer utility functions and, as in Debreu (1952b), used the Eilenburg-Montgomery generalization of Kakutani’s fixed point theorem. McKenzie started from Koopmans and the Menger Colloquium papers of Wald and from von Neumann ([1937] 1945), assumed demand functions, and used the Kakutani fixed point theorem (Kakuktani, 1941), which he had encountered in a Cowles Commission Discussion Paper by mathematician Morton Slater (McKenzie, quoted in Weintraub, 2011, 201). Later Debreu (1959) and McKenzie (1959) developed still more general existence proofs. McKenzie (1960) and Arrow, working with Leonid Hurwicz of Cowles (Arrow and Hurwicz, 1958; 1960; 1962; Arrow, Block and Hurwicz, 1959), examined weak gross substitutability and the weak axiom of revealed preference as conditions for stability of general equilibrium (also the subject of Nikaido’s articles from 1959 to 1964), so McKenzie’s research continued to move in parallel to the work of Arrow and Debreu on general equilibrium, but the general equilibrium papers of all three scholars had their roots in the Cowles Commission in Chicago at the start of the 1950s.

4. GE at Cowles after Debreu’s Departure: Scarf and Computable General Equilibrium, Shubik’s Critique

  • 22 Another contributing factor was proximity to Kakutani and his students in fixed-point theory in Yal (...)

20Herbert Scarf’s Cowles Monograph on Computation of Economic Equilibria (1973) created the field known variously as applied, computable or numerical equilibria. In the spirit of Fisher’s dissertation, as Scarf (1967) emphasized, Scarf went beyond proving by contradiction that at least one equilibrium vector of prices and quantities must exist, to devising an algorithm that would compute the actual values of such an equilibrium, a constructive proof of existence. The research program initiated by Scarf and his doctoral students led to a series of conferences that eventually became an annual event at the Cowles Foundation, producing such conferences volumes as Scarf and Shoven (1984) and Kehoe et al. (2005). Before turning to computable general equilibrium, Scarf had already advanced general equilibrium theory by finding “reasonable” examples of general equilibria that were globally unstable (Scarf, 1960), contrary to conjectures of Debreu (1959) and Arrow, Block and Hurwicz (1959), and by collaborating with Debreu on deriving a limit theorem for the core of an economy (Debreu and Scarf, 1963), showing that the core converges to the set of competitive allocations, without lump sum income redistribution, as the economy is replicated. Scarf’s research program, and the doctoral students that he trained, meant that the Cowles Foundation at Yale remained central in general equilibrium research22 even after Debreu departed for the University of California at Berkeley and more than a century after Fisher’s dissertation and hydrostatic simulation model. The editors of Kehoe, Srinivasan and Whalley (2005, 5), all Yale PhDs, emphasized that “A feature that characterizes the research of the Yale school of AGE [applied general equilibrium] modeling—and distinguishes it from some other AGE modelers—is its heavy interaction with the general equilibrium theory of Arrow, Debreu, McKenzie, and Scarf. Members of the Yale school rely on rigorous theory to guide the development of their models, and they carefully modify and develop new theory when the existing theory is not adequate for their particular applications.” Scarf’s colleague at the Cowles Foundation, Truman Bewley, who in his dissertation and first articles in the early 1970s had extended proofs of existence of general equilibrium and of equivalence of the core and the set of equilibria to infinitely-dimensional commodity space and a continuum of agents, worked on General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory (2007).

21But not all at the Cowles Foundation embraced Walrasian general equilibrium as a research program, either the theory expounded in Debreu’s Theory of Value (1959) or the computable version pioneered by Scarf. Already when reviewing Debreu (1959) in the Canadian Journal of Economics and Political Science, Princeton-trained game theorist Martin Shubik (1961, 133) was moved to “suggest that the future development of economic theory will rest heavily upon the utilization and exploration of assumptions radically different from those employed in this work. At the level of microeconomics there is a necessity for a better model of the economic actor than homo economicus. Economic stability may well depend upon the enforceability of an equilibrium by sets of players larger than one.” Shubik’s criticism echoed the hostile review of Hicks’s Value and Capital by Shubik’s teacher Oskar Morgenstern. In an article whose title paralleled that of Oulès (1950b), Shubik (1975) later dismissed the classical general equilibrium model as “incomplete and not adequate” for the reconciliation of microeconomics with macroeconomic analysis of a monetary economy. Starting in 1970, his monumental Theory of Money and Financial Institutions began appearing as Cowles Foundation Discussion Papers and as journal articles reprinted as Cowles Foundation Papers, eventually revised and assembled as two volumes in 1999 plus a third volume in 2010 (Shubik, 1999-2010), offering game-theoretic foundations for a theory of monetary economy in place of Arrow-Debreu-McKenzie general equilibrium.

5. Conclusion

22General equilibrium analysis reached North America through independent re-invention by Irving Fisher in his Yale dissertation co-supervised by J. Willard Gibbs, followed promptly by Fisher’s energetic efforts to draw attention to the European mathematical economists whose work he had overlooked (Fisher, 1892; Walras, 1892; and, for partial equilibrium, Cournot, [1838] 1897; Fisher, 1898; 1938). He also acted to establish communication with the European theorists through personal contact starting in 1893-94 and through publications (Fisher’s first four journal articles appeared in Edgeworth’s Economic Journal). Such European followers of Walras and Pareto as Jacques Moret (1915) and Wladyslaw Zawadzki (1914) took an interest in Fisher (1892), which Moret translated into French, with Ragnar Frisch discovering Fisher’s dissertation in Moret’s translation. Beyond re-inventing indifference curves and the system of equations for general equilibrium and considering the conditions for integrability of the utility function, Fisher (1892) pioneered computable general equilibrium (and computation more generally) in the era before electronic computers, with his hydrostatic mechanism for simulating determination of equilibrium prices and quantities, a contribution celebrated by Herbert Scarf (1967), the founder of modern computable general equilibrium.

23Fisher made a further contribution by sharing with Ragnar Frisch and Charles Roos in the creation of the Econometric Society and in supporting Alfred Cowles’s creation of the Cowles Commission and Cowles’s funding of Econometrica, edited by Frisch. These developments created a space for mathematical economics within an economics discipline that was then largely nonmathematical. This space for mathematical economics was especially important after upheavals in Europe eliminated or disrupted such forums as Menger’s Vienna colloquium, Kondrat’ev’s Moscow business cycle institute or the Archiv für Mathematische Wirtschafts- und Sozialforschung. Despite the presence of Fisher, Karl Menger, Jacob Marschak and Abraham Wald, general equilibrium was not prominent at the Cowles summer conferences in Colorado. But general equilibrium analysis was undertaken in international trade theory by Theodore Yntema (1932), who became the research director of the Cowles Commission when it moved to Chicago in 1939, and in a Cowles monograph by Yntema’s student Jacob Mosak (1944). Pathbreaking work on the existence and stability of general equilibrium was carried out in the 1950s by three scholars closely associated with the Cowles Commission (at Chicago to 1955) and Cowles Foundation (at Yale from 1955): Kenneth Arrow, Gerard Debreu and Lionel McKenzie. Herbert Scarf contributed to this theoretical literature (with examples of globally unstable equilibria and, with Debreu, a limit theorem on convergence of the core to set to competitive allocations), but then reestablished the link to Fisher’s hydrostatic mechanism (see Scarf, 1967), creating the field of computable or applied general equilibrium, with a recognizable Yale or Cowles approach to the field. At the same time, Scarf’s Cowles colleague Martin Shubik criticized Arrow-Debreu-McKenzie general equilibrium from a game theoretic perspective whose roots went back to Edgeworth (1881).

Presented at the 10th conference of the International Walras Association, University of Lausanne, 13-14 September 2019. I thank Amanar Akhabbar, Annie L. Cot, Cléo Chassonnery-Zaïgouche and Harro Maas for helpful comments at the conference, David Sarech for his presentation which drew my attention to the writings of Firmin Oulès, and two anonymous referees for helpful comments.

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Notes

1 The Cowles Commission became a foundation when Alfred Cowles 3rd provided an endowment in place of an annual gift, at the time of the move from the University of Chicago to Yale in 1955. Yale had first negotiated for the Cowles Commission to move from Colorado in 1937.

2 After receiving his PhD in 1891, Fisher was an assistant professor of mathematics at Yale for three years before transferring to economics. He taught courses and wrote introductory textbooks in calculus and geometry as well as giving a course on “The Mathematical Theory of Price” based on his thesis.

3 Samuelson made that statement in 1967 in a volume in honor of Fisher, where praise of Fisher was to be expected, but already in an article in 1950 he had hailed Fisher (1892) as “perhaps the best of all doctoral dissertations in economics” (Samuelson, 1950, 355).

4 Distance and publication in obscure local journals were not the only barriers to communication: Albert Einstein formalized Brownian motion for particles in 1905 without knowing that Henri Poincaré’s student Louis Bachelier had done so for asset prices in a 1900 Paris doctoral dissertation, published in the annals of the French Academy of Sciences.

5 The machine is no longer extant and perhaps was lost when Fisher’s financial reverses forced him to give up his house for an apartment. Brainard and Scarf (2005) reported on their attempt to reconstruct the mechanism.

6 Except for Zawadzki (1914) and the French translations of Fisher and of Auspitz and Lieben, these books were unknown to Batson’s Select Bibliography of Modern Economic Theory 1870-1929 (1930). Fisher reviewed Suret’s 1914 translation of Auspitz and Lieben in the American Economic Review in 1915. Frisch encountered Fisher’s dissertation through Moret’s French translation while Frisch was studying in Paris (see Dupont-Kieffer, 2013 and Dimand, 2019b on Fisher, Frisch and their shared interest in trying to measure marginal utility).

7 “Cette étude est dédiée à I. FISHER auquel la théorie de capital, du revenu et du taux de l’intérêt doit tant de progrès, en témoignage de notre profonde et respectueuse admiration.” As in that dedication, Fisher’s early work on general equilibrium went unmentioned in the new introduction Allais added in 1998 (44), where he spoke of his 1947 chapter on money and interest having been “très largement influencée par mes réflexions sur les écrits d’Irving Fisher sur l’intérêt, la monnaie et le capital … En fait, je ne saurais trop souligner ici ma dette envers Irving Fisher, l’un de mes maîtres à penser avec Vilfredo Pareto” (italics in original).

8 A referee notes that Fisher’s dissertation was mentioned by Allais in 1943 in an earlier book, A la Recherche d’une Discipline Economique, whose dedication was shared by Fisher, Walras, Pareto and Divisia.

9 The society had less than twenty-two dollars in assets when Cowles became treasurer in April 1932.

10 Wald’s proof was less general than those of Arrow and Debreu and of McKenzie “since Wald assumes fixed proportions among the inputs and the single output of every process” and assumed demand functions instead of deriving them from utility maximization (Arrow and Debreu, 1954, in Debreu, 1983, 95).

11 The RAND Corporation translated the two Wald papers as part of its research on linear programming and circulated them at the 1949 Cowles Commission conference on activity analysis but they were not cited by contributors to the conference volume (Koopmans, ed., 1951), in contrast to numerous citations on von Neumann ([1937] 1945). See Düppe and Weintraub (2016, 647).

12 Arrow, in Arrow et al. (1991, 12), mentioned that Menger, then teaching mathematics at the Illinois Institute of Technology, occasionally attended Cowles Commission seminars after Cowles moved to Chicago in 1939. For example, Menger presented a paper on “Probabilistic Theory of Relations” in the Cowles seminar in November 1951.

13 Although Triffin taught at Yale for two decades after the Cowles Foundation moved there in 1955, his post-dissertation research was in international monetary economics and he did not return to general equilibrium analysis or mathematical economics. Francis Dresch, a postdoctoral researcher in mathematics at the University of California at Berkeley, where he had studied with Griffith Evans, spoke at the 1939 and 1940 conferences about multi-equation models of business fluctuations, but this work was related to macroeconomic modeling rather than Walrasian general equilibrium. Lawrence Klein (1985, 12) recalled that while at the Cowles Commission from 1944 to 1947 he had extensive discussions with Jacob Marschak about the aggregation problem: “In these discussions, I fell back on the work of my first undergraduate teacher in mathematical economics at Berkeley, Francis Dresch, who developed index-number theory to show how his teacher’s research (Griffith C. Evans, a founding member of the Econometric Society) micromodel, could be aggregated from the theory in Evans’ work. This anticipated much modern work with Divisia Indices” (see Dresch, 1938).

14 Lionel McKenzie recalled that “I was present [as a Princeton graduate student between 1939 and 1941] when von Neumann presented his growth model to the Princeton graduate economics seminar. … However as Morgenstern [later noted] the paper was not understood by anyone present, and so far as I am concerned, he is right” (Weintraub, 1985, 97). Von Neumann had first presented his circular model of an economy growing at a uniform rate to the Princeton Mathematical Society in 1932 (he alternated semesters in Berlin and Princeton from 1930 until 1933, when he joined the Institute for Advanced Study in Princeton), so his talk to the economics graduate students was a second presentation of his model at Princeton. He also gave a popularized exposition of his game theory paper at Princeton in 1937 (see Anonymous, 1937).

15 The first of von Neumann’s 1928 minimax papers (1928a, much less known than the longer article later the same year in German, 1928b), written in French and communicated by Emile Borel to the French Academy of Sciences, is translated in Ben-El-Mechaiekh and Dimand (2010), together with Jean Ville’s 1938 non-topological proof of the minimax theorem (the basis of the proof used by von Neumann and Morgenstern in 1944) and Borel’s comments on Ville’s proof. The first proof of the minimax theorem, announced in von Neumann (1928a) and presented fully von Neumann (1928b), was challenging, difficult to follow and involved both a lemma restated as a fixed point theorem by Kakutani (1941) and the first statement of quasiconvexity; see Ben-El-Mechaiekh and Dimand (2011) for a simpler proof.

16 Nor, judging from the papers they wrote at the time, in New York where Marschak and Neisser were colleagues in the New School’s University in Exile from 1940 until Marschak moved to the Cowles Commission in Chicago at the end of 1942 (they had previously been colleagues with Leontief in Kiel in 1928-30) and where Marschak was in contact with Wald (teaching statistics at Columbia) through an NBER-sponsored weekend seminar in econometrics organized by Marschak and Oskar Lange (visiting Columbia from the University of Chicago).

17 Arrow (in Arrow et al., 1991, 10-11), in a paper given in June 1983 on the 50th anniversary of the Cowles Commission, wondered how von Neumann thought of alternative activities for producing the same goods and multiple outputs from activities when the only economist cited in von Neumann ([1937] 1945) was Gustav Cassel: “But Cassel’s formulation has only fixed coefficients of production and indeed in a very primitive way; it does not even allow for circular flow. Perhaps the activity analysis formulation of production was simply obvious to a genius like von Neumann.” But Marschak (1934) went well beyond Cassel’s 1899 version of Walras’s system of equations in those respects (see Dimand and Hagemann 2020a) so, to the extent that the ideas of Marschak (1934) were already present in Marschak’s 1928 Berlin seminar presentation, von Neumann may have been influenced by Marschak’s talk beyond finding counting equations and unknowns inadequate for showing existence of equilibrium, while the final published version of Marschak (1934) may also have been influenced by von Neumann’s comments at the 1928 seminar. See also Marchionatti (2019, 1381, 1390) regarding possible influence on von Neumann ([1937] 1945) by Robert Remak, a Berlin privatdozent in applied mathematics from 1929 to 1933 (see the excerpt from Remak’s 1929 article translated in Baumol and Goldfeld, 1968, 271-277), and by Wassily Leontief’s Berlin dissertation (Leontief, 1928).

18 Neither Yntema (1932) nor Mosak (1944) cited Fisher (1892). Both referred primarily to Edgeworth, Pareto and Marshall for early equilibrium analysis of international trade, with Yntema also citing books by Cournot, Walras, Pantaleoni and Auspitz and Lieben.

19 The Cowles Commission became the leading center of general equilibrium research just as the University of Lausanne was moving away from any such role. Firmin Oulès, holder of the chair formerly held by Walras and Pareto and editor of selections from their writings (Oulès, 1950a), strongly preferred the social and applied economics of the first Lausanne school to their pure economics, and sharply criticized their general equilibrium analysis as insufficient and inappropriate (Oulès, 1950b; 1950c). Mathematical economics in Continental Europe outside Switzerland, such as in Karl Menger’s Vienna colloquium, was disrupted by the upheavals and emigrations of the 1930s. The Archiv für Mathematische Wirtschafts- und Sozialforschung, founded in 1935 (two years after Econometrica) and initially a venue for articles by such notable economists as Erich Schneider, Heinrich von Stackelberg and Jan Tinbergen, declined in quality and lost political independence, finally ceasing publication in 1943.

20 In 2009, McKenzie wrote to Roy Weintraub (2011, 209) that “Actually I did visit the Cowles Commission in Chicago when Debreu was there and working on existence, but he kept this fact secret from me. I asked him what he was working on and he refused to say. The first thing I knew about his work was when we both presented papers on existence to the Chicago meeting of the Econometric Society in [December] 1952.” Debreu (1951), written before Debreu knew of Arrow’s preliminary work on proving existence of general equilibrium, and Debreu (1952a), written after he read Arrow (1951b), were circulated as Cowles Commission Discussion Papers, and Arrow (1951b) and Debreu (1952b) were reprinted as Cowles Commission Papers but, according to McKenzie’s recollection, were not noticed by him.

21 Weintraub (2011, 213, n13) reports that “Nikaido had independently developed a proof of existence of a general competitive equilibrium using the Kakutani theorem at that time [when his mentor Takuma Yasui heard the Debreu and McKenzie papers in Chicago in December 1952], but it was not until he read McKenzie’s paper in 1954 that he believed his own paper might find a place in an English-language journal. His difficulty getting his paper published led to his belief that he might have been ill-treated.” However, Kazuo Nishimura and Richard Day, in their biographical foreword to Nikaido (1996, ix) state that Nikaido’s existence proof “which was published in 1956, was first presented at the annual meeting of the Japan Association of Economics and Econometrics in the autumn of 1954, the same year that the existence proofs of McKenzie and Arrow and Debreu appeared” (but after they were published and nearly two years after Debreu and McKenzie spoke at the Econometric Society, and even longer after the preliminary, less general existence proofs of Arrow, 1951b and Debreu, 1952b were reprinted as Cowles Commission Papers) and “led to a visiting appointment at Stanford, 1955-56, at the invitation of Kenneth Arrow” so the ill-treatment is not evident. Nikaido (1954) had published an extension of the von Neumann growth model in the Econometrica issue preceding that with McKenzie (1954a), so he was not entirely a distant outsider.

22 Another contributing factor was proximity to Kakutani and his students in fixed-point theory in Yale’s Mathematics Department at 12 Hillhouse Avenue, a few doors from the Economics Department at 28 Hillhouse and the Cowles Foundation at 30 Hillhouse. The presence of Bayesian statisticians Leonard Jimmie Savage and I. Richard Savage at the Statistics Department at 24 Hillhouse in the 1960s mattered for econometrics at Yale and for attention to the (L.J.) Savage axioms for rational choice. As the home of the fractalist Benoit Mandelbrot, Yale’s Mathematics Department also generated ideas, such as emphasis on fat-tailed probability distributions for asset price movements, less in accord with the mainstream economics of the Cowles Foundation.

23 In 1947 the Cowles Commission initiated three series of discussion papers: in economics, starting with no. 201, statistics starting with no. 301, and mathematics starting with no. 401. When the economics series reached number 299 in 1950 (as surely could have been predicted), the economics series jumped to no. 2001 in 1951.

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Robert W. Dimand, « Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis »Œconomia, 11-2 | 2021, 253-280.

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Robert W. Dimand, « Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis »Œconomia [En ligne], 11-2 | 2021, mis en ligne le 01 juin 2021, consulté le 22 septembre 2021. URL : http://journals.openedition.org/oeconomia/10940 ; DOI : https://doi.org/10.4000/oeconomia.10940

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Robert W. Dimand

Department of Economics, Brock University, rdimand@brocku.ca

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