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Léon Walras: What Cutes Know and What They Should Know

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Part of the book series: The European Heritage in Economics and the Social Sciences ((EHES,volume 11))

Abstract

The general idea among contemporary university-trained economists (“cutes”) of what Léon Walras (1834–1910) has contributed to analytical economics may be summarised in modern notation as follows: Let a system of equations be given: e(p) = 0, where the symbol p denotes an n-dimensional vector of prices of goods brought to the market and e is a vector-valued function of the prices representing the n excess demands in the market for the goods. The equation expresses market equilibrium and the generally accepted view seems to be that there is a so-called auctioneer who takes care that such an equilibrium will occur. To that end, he, the auctioneer, announces an initial vector p′ of prices. The people who bring the goods to the market in order to exchange (part of) them for other goods react on these initial prices by establishing certain quantities of goods demanded or supplied.

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Notes

  1. 1.

    Walras’s great-grandfather was born in Arcen in the Southern part of The Netherlands, under the name Andraeas Walravens and migrated to the South of France. His son became a kind of lower magistrate in the city of Montpellier. In between, the name was shortened into Walras. Because of the Dutch origin of the name, the s in Walras has to be pronounced (see Walras 1965, Letter 999).

  2. 2.

    After the first edition of the Éléments, three revised editions followed, in 1889, 1896 and 1900. Walras did not live to see in print the revisions he made after the fourth edition. These appeared in the posthumous, fifth edition of 1926. An English translation, by William Jaffé, of the latter edition appeared in 1954. From 1987 onwards, the “Centre Auguste et Léon Walras”, Lyon, republished (with Economica, Paris) Léon Walras’s complete works in nine volumes as part of the fourteen volumes of AUGUSTE AND LÉON WALRAS, ŒUVRES ÉCONOMIQUES COMPLÈTES, completed in 2005. See also the Walras bibliography in Walker 1987, where 239 titles are mentioned.

  3. 3.

    Walras expressed it as follows in a letter to W. Lexis du 17 mars 1883 (Walras 1965, letter 548):

    (....) il m’a semblé que vous me considériez comme un partisan de la libre concurrence absolue (en raison de ce fait que j’étudie très attentivement et très minutieusement les effets de la libre concurrence). Quoi qu’il en soit, je tiens à vous faire savoir que, tout au contraire, c’est plutôt le désir de repousser les applications mal fondées et inintelligibles de la libre concurrence, faites par des économistes orthodoxes qui m’a conduit à l’étude de la libre concurrence en matière d’échange et de production. Un médecin qui aurait analysé dans le dernier détail les effets physiologiques d’une substance serait à la fois, par ce fait, très partisan de son emploi dans certains cas et très opposé à cet emploi dans certains autres cas. Telle est ma position (…).

  4. 4.

    The hierarchy is not complete (see Van Daal 1994; Van Daal and Jolink 1993b, Chaps. 14–16).

  5. 5.

    See Van Witteloostuijn and Maks (1988 and 1990).

  6. 6.

    In the case of Walras, a non-econometric, or perhaps pre-econometric case, we mean with the expression “rationality in Muth’s sense” that economic agents are (supposed to be) at least as clever as the economist who is modelising their behaviour concerning the formulation of expectations for the (near) future. See Muth (1960, 1961). Walras’s agents seem to be much more stupid.

  7. 7.

    See Van Witteloostuijn and Maks (1988 and 1990), Mckenzie (1987): 503 and Van Daal and Jolink (1993b): 74.

  8. 8.

    Walras defined this as follows (Éléments, § 327): “Progress (…) consists in a diminution of the raretés of the final products along with an increase in population”. See also Lionel Robbins’s seminal An Essay on the nature & Significance of Economic Science (Robbins 1932), where scarcity “means limitation in relation to demand” (p. 46). This book perhaps caused the breakthrough of the neo-classical (Walrasian) definition of economics: “Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses” (p. 15.).

  9. 9.

    See for similar wordings Keynes’s General Theory (Keynes 1936, Chap. 13).

  10. 10.

    By introducing present utility of the expectation of future additional income, Walras was able to bring himself “as close as possible to the dynamic point of view” in his formal models (Éléments, editions 4 and 5, §272). Here is meant “inter-period dynamics”, in contradistinction to the “intra-period dynamics” of tâtonnement. It is again to be emphasised that the expected future income is based on a very simple myopic expectations scheme: agents assume that the equilibrium prices of the period considered will also hold in the future; see Maks and Van Wittteloostijn (1987, 1988, 2001).

  11. 11.

    While staying within the realm of constant returns to scale.

  12. 12.

    And later; see Bowley (1924).

  13. 13.

    Or (Schumpeter 1954: 1006): “Of all the unjust or even meaningless objections that have been levelled at Walras, perhaps the most unjust is that he believed that the existence question is answered as soon as we have counted ‘equations’ and ‘unknowns’ and found that they are equal in number”.

  14. 14.

    See also Van Daal and Jolink (1993b), Fig. 4.5 (p. 26).

  15. 15.

    See Van Daal (1998), where proofs are presented for all Walras’s models.

  16. 16.

    Walras supposed that demand and supply curves are so located and shaped that they intersect.

  17. 17.

    Indeed, later authors have elaborated on it, proving rigorously the convergence of the sequence p 1, p 2, p 3, … of prices to equilibrium prices. Allais (1943, vol. 2: 489 ff.) was the first to provide in this way a proof of the existence of equilibrium in the case of exchange only: he had to impose the condition of so-called gross substitutability. See also Morishima (1977), Chap. 2.

    Nevertheless, there is somewhat more to say. Walras assumes that his rareté functions only depend on the quantity of the own commodity and are always (dis)continuously decreasing in that quantity. This can be seen in all graphs depicting rareté curves, (Éléments, §§ 74–84). Hence, the rareté functions do not shift if the quantities of the other commodities change. Starting from this concept and assuming that the marginal utility elasticities of all commodities vary (on the average) in their normal range between 0 and −1, it can be proved that gross substitutability holds and that the prices p 1, p 2, p 3, … indeed converge to equilibrium prices (see Maks 2006).

  18. 18.

    For that same reason, Walras had discarded from the outset the possibility of disequilibrium transactions in the case of exchange only.

  19. 19.

    Walras’s French word was “bon”. Jaffé translated it as “ticket”. We prefer the translation “pledge”, proposed in Walker (1987a).

  20. 20.

    For a comprehensive and authoritative discussion of all tâtonnements and of Walras’s way of trying to embed this in an institutional framework, we refer to Walker (1996). In particular, we refer once more to Walker’s explanation of how the market agents can do without an auctioneer.

  21. 21.

    At the same time, it means a complete change of what happens during a period. The models with production (i.e. all models after those of pure exchange) of the third edition describe quite other “events” during a period than those of the fourth.

    Walker, too, considers the new tâtonnement as unfortunate. He appears to be a partisan of its predecessor. Personally, we think that both are problematic (see Van Daal 2000).

  22. 22.

    The mechanism that transforms a price vector into the subsequent one differs in most modern textbooks from that invented by Walras himself. Walras’s procedure works consecutively, price by price, and the process goes through a number of intermediate situations. In the textbooks, all prices change mostly instantaneously and simultaneously in one single non-stop flight from the initial value to the equilibrium prices (see Van Daal 2000).

  23. 23.

    Presumably, Walras meant here that enterprises interested in producing and distributing, say, gas under monopoly in some city, meet in an auction to try to get the concession. This auction might be organised as follows. The interested parties are invited by the auctioneer to propose a price at which they will produce and supply the product. The price proposed by the first bidder will perhaps exceed the cost price of one or more of the parties. Then the auctioneer tries to solicit a lower selling price. Let us suppose that somebody makes such a bid, possibly still above one or more cost prices. A third selling price might then be proposed, and so forth. Under certain conditions, this process might converge to a bid equal to the cost price of the most efficiently producing party. Here, we cannot speak of a Dutch auction, where the auctioneer starts with a high, unacceptable price and then proposes prices gradually lower and lower and where the first participant who calls “mine” at a certain price is bound by it. In an “English auction”, the auctioneer tries to solicit higher and higher bids from the participants, till nobody wants to make another bid. The highest bidder is then bound by his bid. Both systems are aimed at the achievement of a final price as high as possible. See, for instance, Vickrey (1961). The procedure indicated above in the case of Walras might perhaps be called an “inverse English auction”.

  24. 24.

    Gossen (1854), pp. 250–273; Chap. 23 of the English translation.

  25. 25.

    Van Daal and Jolink (1993a, b), pp. 120–126; see also Van Daal (1999).

  26. 26.

    Albert Jolink (1991, 1996) perhaps was the first to present a complete view of Walras’s oeuvre from an evolutionist standpoint with the Social Question as the continuous thread running through it.

  27. 27.

    Or, rather, silver token, because its real value must be somewhat less than its nominal value.

  28. 28.

    This meagre result is the more striking because Marshall has read the Éléments. The copy of the book in the Oxford University Library reveals Marshall’s hand written notes (stopping at page 169).

  29. 29.

    E.g. the unchanged 1924 edition; the book was first published in 1907.

  30. 30.

    And others like, e.g. O. Lange. The original version of Barone’s paper was published in 1908, in Italian. It became generally known after the publication of its English translation, “The Ministry of Production in a Collectivist State” in F.A. von Hayek (ed.), Collectivist Economic Planning (Barone 1935).

  31. 31.

     L. Von Mises, “Die Wirtschaftsrechnung im Sozialistischen Gemeinwesen” translated as “Economic Calcualation in the Socialistic Commonwealth” in F.A. von Hayek, ed., Collectivist Economic Planning (Von Mises 1935).

  32. 32.

    Von Mises further developed his reputation as a critic of socialism. He published in 1932 his revised second edition of Die Gemeinwirtschaft, Untersuchungen über den Sozialismus. Since we know that Walras was advocating State ownership of the land, one might expect some reference in Von Mises’s book to this idea. But in the whole book, one cannot find any reference to Walras. Even in discussing “Das Gemeineigentum an den Produktionsmitteln” (pp. 25 ff.), he does not refer to Walras.

  33. 33.

    See Manuel d’économie politique (1981[1909]), translated from his Manuale di economia politica (1906).

  34. 34.

    Here, Schumpeter emphasises that it is a misunderstanding to think that Walrasian micro-analysis is in need of a supplement by a Keynesian income or macro-analysis.

  35. 35.

    Here, Schumpeter stresses that Walras was prepared to admit that capitalists lend money and not capital goods. He concludes that this observation is important to see the affinity between the Walrasian and Keynesian systems.

  36. 36.

    In this note, Schumpeter warns us against making individual demand only dependent of the own price and income for pedagogical reasons. This deeply obscures Walras’s approach and, in the end, it does not help the student to understand the relation between Keynesian and Walrasian economics.

  37. 37.

    In this note, Schumpeter points out that it is not true that Walras neglected the influence of income, but Keynes neglected the influence of prices.

  38. 38.

    Here, Schumpeter observes that the precautionary and the speculative motive for holding cash can be inserted in the Walrasian theory.

  39. 39.

    See Wicksell’s “Zur Zinstheorie” in “Die Wirtschaftstheorie der Gegenwart” ed. H Mayer, III, 1928 (Wicksell 1928).

  40. 40.

    And on Pigou, who also adhered to non-neutrality of money in his Theory of Unemployment (Pigou 1933).

  41. 41.

    Or to the related considerations in Pigou (1933).

  42. 42.

    Probably because the Keynesian analysis neglects relative prices.

  43. 43.

    Together with a substantial decrease in weight of Keynesian macro-economics.

  44. 44.

    Pascal Bridel devoted his Money and General Equilibrium Theory (Bridel 1997) to this important part of Walras’s oeuvre; see also Van Daal and Jolink (1993b), Chaps. 10–16.

  45. 45.

    This is completely in line with the interpretation of Walras by Hicks (1934). Hicks claims to be the first to analyse a sequence of temporary equilibria (Hicks 1939). The previous sections have clarified that this claim is unjust.

  46. 46.

    See Walker (2001). This collection (65 articles in two volumes) is the third of its kind. Mark Blaug published a volume with 25 articles in 1992 and in 1993, John Cunningham Wood a three volume set of 68 papers. Further, the volume with 19 articles by William Jaffé on Walras, edited by Donald: Walker (1983), should be mentioned. Altogether, these bundles contain 148 different articles. Walker’s two collections stand out because of excellent editorial work, especially the original introductions.

  47. 47.

    See, e.g. the mentioned volumes of Walker (2001), but also Schinkel (2002).

  48. 48.

    See MacCloskey (1985), 1994) and also Henderson (1995).

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  1. School of Business and Economics, Department of Economics, Maastricht University, 616, 6200 MD, Maastricht, The Netherlands

    J. A. Hans Maks

  2. Triangle, University of Lyon-2, Lyon, France

    Jan van Daal

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    Jürgen Georg Backhaus

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Maks, J.A.H., van Daal, J. (2012). Léon Walras: What Cutes Know and What They Should Know. In: Backhaus, J. (eds) Handbook of the History of Economic Thought. The European Heritage in Economics and the Social Sciences, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8336-7_18

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