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Walras, Léon

Walras, Léon

Early economics

Marginal utility theory

Theory of general equilibrium

Later life and work

WORKS BY WALRAS

SUPPLEMENTARY BIBLIOGRAPHY

Léon Walras (1834-1910), whose full name was Marie Esprit Léon Walras (the final “s” is sounded), is celebrated among economists and econometricians as the first to have formulated a multiequational general equilibrium model of economic relationships. He was born on December 16, 1834, in Évreux, a provincial town of Normandy, France. Although he spent more than half his adult life in Switzerland, he retained his French citizenship. His patronymic was not French but a corruption of the Dutch surname of his greatgrandfather Andreas Walravens, a journeyman tailor who migrated in 1749 from what is now County Limburg in the Netherlands to Montpellier in the south of France. There the Walras family remained in modest obscurity until Antoine Auguste Walras, Léon’s father, was accepted as a student of the École Normale Supérieure in Paris, where he was a classmate of Antoine Augustin Cournot. Auguste Walras, author of De la nature de la richesse, et de I’origine de la valeur (1831), was an economist in his own right, although he failed to obtain a chair in economics and wasted his years as a minor administrator in the French educational system. His career was botched partly because of his outspoken anticlericalism, combined with a singular ineptitude in dealing with his hierarchical superiors, and partly because of his untimely advocacy of a utility theory of value, of land nationalization, and of radical tax reforms. Walras inherited his father’s traits of character in all too generous measure. He also adopted his father’s unorthodox economic views; indeed, his father was the only teacher of economics Walras ever had. His mother, Louise Aline nee Sainte Beuve, the daughter of a notary of Evreux, came from a locally prominent family that at times claimed the nobiliary particle de but was not of the same line as that of the famous literary critic Sainte Beuve. From his mother, Walras inherited the frugal, calculating temper of the Normans and, eventually, 100,000 francs.

Walras’ early education followed the usual course for youths of his station, culminating in two baccalaureate degrees, one in letters, in 1851, and the other in science, in 1853. His curriculum included mathematics through high-school algebra and analytical geometry but nothing much beyond. In fact, his mathematical attainments proved insufficient to enable him to gain entrance to the école Polytechnique. Finally, in 1854, he was admitted as a nonresident student to the École des Mines in Paris. With Bohemian insouciance he neglected his engineering studies, which he found distasteful, and turned to literature. In 1858 he published a novel, Francis Sauveur, and in 1859 a short story, “La lettre,” in the Revue francaise. These pieces, although lacking in literary distinction, were not without significance, for they contained ideas inspired by the revolution of 1848 and, in most unlikely contexts, elements of economic reasoning that were clearly the first fruits of Walras’ upbringing in an economist’s household. Realizing that he was not meant for a literary career, he promised his father in the summer of 1858 that he would devote his life to economics.

Professional openings for an economist in France of that epoch were extremely rare and were all the more inaccessible to Walras not only because he lacked the requisite formal university training but also because he stood outside the charmed circle of official French economists, who formed a closed corporation dedicated to the existing political and social order and to the dogma of unmitigated economic individualism. But Walras’ need to make a living was pressing, particularly when he set up house around 1859 with an unmarried mother, Celestine Aline Ferbach, and had twin daughters by her in 1863, one of whom died in infancy. It was not until 1869 that he married her, legitimizing her son and his own surviving daughter, Marie Aline. He tried his hand at journalism but was soon discharged because of the independence of his opinions. He worked for a while at the secretariat of the Chemin de Fer du Nord. Then, in 1864, he became managing director of a bank for cooperatives in which Léon Say was interested, but the bank was compelled to liquidate in 1868. While he was directing the bank, Walras wrote and lectured on the organization of cooperatives, which were looked upon in the 1860s as an antidote to the revolutionary threats of the working classes. From 1866 to 1868 he and Léon Say edited a short-lived monthly cooperative organ, Le travail. Finally, before receiving his call to the Academy (later the University) of Lausanne, he was corresponding secretary for a private banking establishment in Paris.

During the 12 years between his departure from Ecole des Mines and his entrance upon an academic career in Switzerland, Walras was writing and cogitating on economic subjects. At an early stage he formulated in broad outline the whole program of his intellectual lifework: a trilogy made up of pure economics, applied economics, and what he called “social economics” (économie sociale). Pure economics was conceived on the analogy of pure mechanics and was to consist in an explanatory model, mathematical in structure, depicting a comprehensive network of relationships rigorously derived from the assumption of supposedly perennial, or “natural,” economic forces independent of institutional arrangements. Applied economics was thought of in terms of the application of pure theory to problems of production, with a view to determining, in the classical tradition, the forms of industrial organization most conducive to the maximization of social output. While applied economics hovered between the positive and the prescriptive design, social economics was to be unreservedly normative and concerned with principles of “justice” (essentially Aristotelian and Thomistic) which should govern not only the distribution of wealth, especially between the state and private individuals, but also exchange.

Early economics

Before going to Lausanne, Walras made little or no progress in pure economics, publishing nothing on the subject. Nevertheless, he made two fumbling attempts, which survive in manuscript, to apply the little mathematics he knew to economic analysis, and he arrived at only one concept of importance, his equation d’échange, a budget equation in all but the name. Nor did he make any advance in applied economics at this time. His attention was almost entirely absorbed in formulating the fundamental philosophical ideas of his social economics. In this period he published his first professional book, L’économie politique et la justice (1860), which was essentially an ideological work based on his father’s views. In 1860, while participating in an international congress on taxation held at Lausanne, he first met the young Swiss lawyer and politician Louis Ruchon-net, who ten years later helped him to obtain his appointment to a newly established chair in political economy at Lausanne.

In a series of public lectures delivered in Paris during 1867-1868 and published under the title Recherche de I’ideal social (1868), Walras expounded his philosophy of social reform based on the metaphysical ideas of Victor Cousin and Etienne Vacherot, calling for a conciliation of interests. Ideological as his position was, he resisted the efforts of his Saint-Simonian friends to enroll him among their number, because their socialism was “unscientific.” He always thought of himself as a “scientific” socialist, with “scientific” reasons for advocating that the state take over (by purchase) whatever private property (land, natural monopolies, railways) could be shown analytically to be inconsistent with the attainment of the relative maximum welfare that free competition, when properly constrained by the inviolable rules of “justice,” would bring about. The state, then, having its own income-producing property, would not—indeed should not—impose taxes, for taxation itself interferes with the beneficent operation of competitive forces. Neither in the Recherche de I’idéal social nor in any other of the pre-Lau-sanne publications did Walras display analytical acumen or give any inkling of what was to come.

On December 16, 1870, his 36th birthday, Walras delivered his first lecture as professeur extraordinaire in the faculty of law of the Academy of Lausanne. Virtually up to the last moment his path toward the realization of this long-cherished ambition had been beset with difficulties. The France—Prussian War, raging in France, made it hard enough for Walras to join his post; earlier, his appointment even for a trial period of one year had been opposed by three of the seven members of the Swiss ad hoc committee charged with the task of appraising candidates for the Lausanne chair of political economy. The minority report, while agreeing that Walras was superior to his competitors for the post, found his writings “communistic"! By 1871 all such fears were allayed and Walras was duly inaugurated as professeur ordinaire—with tenure. Whether only out of caution or out of sheer intellectual curiosity, he initially concentrated upon pure economics, which then became his dominant passion. In fact, when he later resumed writing on questions of policy, it was, as he confessed to a correspondent, mainly because he felt that his articles on current issues would eventually call attention to his analytical work.

Marginal utility theory

Once at Lausanne, Walras began to teach himself calculus, having been shown by Paul Piccard, a professor of mechanics, how to apply the technique of maximization to the theory of utility. Thus, Walras developed his mathematical theory of rareté (marginal utility) and presented the two-commodity case in simplified geometric form in a paper, “Principe d’une théorie mathématique de

l’échange,” which he read before the Académie des Sciences Morales et Politiques of Paris in 1873. This performance was greeted with undisguised hostility. After the publication of this first paper, he was dismayed to learn that W. Stanley Jevons had anticipated him in originating the theory of marginal utility. Walras honorably acknowledged Jevons’ priority, consoling himself with the perfectly just reflection that he had done better than Jevons in establishing a correct relation between utility and demand. Nevertheless, his feelings of jealousy continued to rankle until he discovered that the German economist Gossen, already dead and consequently no longer a potential rival, had anticipated both Jevons and himself in 1854. To forestall further disappointments in his race for priority, Walras hastened his pace, publishing a series of three additional papers in pure economics, the substance of which was embodied in the first edition of his EÉléments d’economie politique pure (1874-1877).

Walras sought to make himself known to economists in France and elsewhere by sending them reprints of his articles and copies of his Éléments, accompanied by letters asking for criticism. His first success was in Italy, where Gerolamo Boc-cardo, Luigi Bodio, and Alberto Errera acclaimed Walras’ contributions with enthusiasm. From Germany, England, Holland, and Denmark he received encouraging responses. In France, however, to Walras’ chagrin, his early work evoked either no comment at all or else outright antagonism, except from Cournot and the philosopher Charles Renouvier.

As time went on, Walras’ economic correspondence assumed enormous proportions: literally thousands of letters passed between him and such of his contemporaries as Foxwell, Marshall, Edge-worth, and Wicksteed in England; Menger, Böhm-Bawerk, and Lieben in Austria; PantaLéoni, Pareto, and Barone in Italy; Charles Gide, Hermann Laurent, Henri Poincaré (on methodology), and Albert Aupetit in France; Bortkiewicz in Germany; Knut Wicksell in Sweden; and John Bates Clark, Irving Fisher, and Henry Ludwell Moore in the United States. He thus became literally an economist’s economist, for it was impossible for him to mold disciples among his law students at Lausanne, who regarded the course in economics as a tiresome superfluity. In other universities the novel mathematical character of his writing repelled the ordinary student, whose training was purely literary, and the marginal utility approach to value outraged the orthodox economists dedicated to the Ricardian cost-of-production approach. Only the elite of the profession took any interest at all in Walras’ innovations, and with them he held a continuous seminar—by correspondence—exchanging criticisms that left their mark on the four successive editions of the Éléments which appeared during Walras’ lifetime.

While Walras had no economic colleagues at Lausanne with whom to take counsel, he did have mathematical colleagues, not only Paul Piccard but also Hermann Amstein, from whom he got all the help he could. When he asked Amstein to formulate the mathematical conditions of minimum cost of production, Amstein in 1877 presented him with an almost perfect marginal productivity model, even using the Lagrange multiplier method; but Walras knew too little mathematics to understand it and Amstein too little economics to appreciate its significance. It was not until after Wicksteed’s Essay on the Co-ordination of the Laws of Distribution appeared in 1894 that Walras filled the empty niche in his theory of production by incorporating Barone’s formulation of the marginal productivity theory into his Éléments, since Amstein’s still remained beyond his ken.

Theory of general equilibrium

For many years Walras thought that his chief title to fame lay in his marginal utility theory, which was certainly more rigorous and elegant than that of either Jevons or Menger. He did not realize the full significance of the unique character of his general equilibrium system until Barone hailed it in the Giornale degli economisti (1894, p. 407) as “the most general, most comprehensive and most harmonious” that had yet appeared. Already in the 1870s, in the first edition of the Éléments, Walras had laid the groundwork for a unified model, comprising the theories of exchange, production, capital formation, and money. In the subsequent revisions of the Éléments, he strengthened the model by applying the principle of utility maximization throughout. Moreover, to link his model to the real world, he followed up each of his successive cumulative submodels describing the static determination of equilibrium with a related quasi-dynamic theory of the emergence (or establishment) of equilibrium via the operation of the competitive market mechanism. He called the process of automatic adjustments of the network of real markets to equilibrium one of tdtonnement, that is, of groping without conscious direction. His argument that the process would culminate, under his assumptions, in a stable equilibrium was, nevertheless, intuitive, without any semblance of a rigorous demonstration. Despite this and other defects, lacunae, and inconsistencies in detail, which were inevitable in so immense a pioneer work produced with primitive mathematical tools, Walras’ general equilibrium model earned for him the supreme encomium of Joseph Schumpeter, who said that “as far as pure theory is concerned, Walras is in my opinion the greatest of all economists” (1954, p. 827).

The idea of general equilibrium was not new with Walras. It had already been enunciated in 1690 by Nicholas Barbon; there were discernible adumbrations of the theory in Petty, Boisguilbert, Cantillon, and especially in Turgot and Quesnay; and an implicit pattern of mutually interdependent relationships underlies the writings of the great classical founders of economics, Adam Smith, Ricardo, and Jean Baptiste Say. It is altogether unlikely, however, that Walras derived direct inspiration for his multiequational model of interdependence from these precursors. He himself liked to give the impression that his father and Cournot had furnished the principal elements of his economic theory, but Cournot had mentioned the interconnection of all the parts of the economic system only to recoil from it as surpassing “the powers of mathematical analysis,” and Auguste Walras had furnished nothing but vague hints of general equilibrium.

The true fons et origo of Walras’ multiequational formulation of general equilibrium was Louis Poinsot’s once famous textbook in pure mechanics, Éléments due statique (1803), which, as Walras confided to a friend in 1901, he first read at the age of 19 and then kept by him as a companion book throughout his life. In Poinsot we find virtually the whole formal apparatus that Walras later employed in his Éléments d’economie politi-que pure. Poinsot’s Éléments de statique bristles with systems of simultaneous equations, some of them equilibrium equations proper and others equations of condition (constraints or definitional identities), and contains the postulate that these systems have determinate solutions if they consist in as many independent equations as unknowns. Isnard’s Traite des richesses (1781)—which Walras rescued from oblivion by inserting it in the list of writings on mathematical economics compiled by Jevons (1871)—also appears to have played a part in shaping Walras’ formulation of his system. Walras praised Isnard for having correctly stated algebraically the inverse proportionality of values to quantities exchanged. Both in his unpublished juvenile essays of the 1860s and in the opening algebraic treatment of exchange in the Éléments, Walras’ simultaneous equations bear a remarkable resemblance to Isnard’s. Notable, too, was Isnard’s anticipation of the Walrasian proposition that the use of a standard unit of account obviates the need for recourse to arbitrage in a competitive, multi-commodity model.

Although Walras was not really indebted to his father or to Cournot for his composite model, his pure theory does bear the sharp imprint of their influence. Walras took over, for better or for worse, a good part of his father’s terminology, his taxonomy, and his conception of the object of economics. From Cournot he first learned the meaning of functional relations between variables; it was precisely his growing dissatisfaction with Cournot’s particular demand function that first led him to seek a wider framework within which to express the quantity demanded of a commodity as a function not of the price of that commodity alone, but of the entire constellation of prices. This was the point of departure for his general equilibrium model.

Later life and work

Soon after the publication of the first edition of the Éléments, Walras’ wife was stricken by a fatal illness and his financial situation deteriorated. His academic salary, which had been raised in 1872 from the initial 3,600 francs per annum to 4,000 francs, still proved inadequate. To eke out the income he required for his family needs and his research and publication expenses, he had to give supplementary courses at Geneva and Neuchatel, to serve as a regular consulting actuary for a Swiss insurance company, to write fortnightly feature articles (under the pseudonym “Paul") for the Gazette de Lausanne, to contribute weighty articles to the Bibliotheque universelle, and to borrow. When in 1879 his old friend Jules Ferry became minister of public instruction in France, Walras thought he had a chance to obtain a university post in his native country and to improve his financial situation. His efforts in this direction proved vain, notwithstanding his offer to help Ferry modernize the whole French university system and, by the same token, pull the teaching of economics out of the law-school rut and give it the status of a science. In 1881 the Academy of Lausanne increased his salary to 5,000 francs. But it was only after his second marriage in 1884 (his first wife having died in 1879), that his financial condition took a substantial turn for the better. His second wife, Léonide Désirée Mailly, a French spinster who had lived for many years in England, brought with her an annuity which more than doubled the income of the Walras household.

Relieved now of private financial worries, Walras returned to his work with a burst of renewed energy. He ventured upon a fundamental revision of his theories of money and capital and took up the cause of monetary reform. In his monetary theory, he substituted the conception of a demand for cash balances (encaisse désirée) for his earlier conception of the demand for money as depending on the volume of transactions to be cleared (circulation àdesservir). As Arthur Marget pointed out, this entailed the substitution of his earlier Fisherian equation of exchange by an equation essentially Keynesian in form (1931). The change was made in the interests of symmetry and over-all coherence in the general model, for now the same primum mobile—the maximization of utility—could operate in the theory of money as in the rest of his system. Walras’ new monetary theory, first announced in his paper “Équations de la circulation” (1899), was very soon incorporated into the fourth edition of the Éléments. Into this edition, he also introduced his revised conception of the role of interest as an equilibrating factor between the aggregate demand for cash balances and the existing quantity of money.

Walras’ revision and extension of his theory of capital formation were similarly motivated. In the fourth edition of the Éléments, in order to avoid the dilemma of either continuing to use his earlier empirical savings function unrelated to the utility maximization principle or of complicating his postulates with time preference functions, Walras chose to consider savings and investment, as he did consumption and production, exclusively at the moment of decision making. He envisaged the decisions theoretically as bearing on a fictive commodity, “perpetual net income” (net of depreciation and insurance charges), each unit of which represents a perpetual yield of one unit of numeraire per annum from whatever assets, human as well as marketable, an individual possesses. This commodity, having a utility function of its own, enters into the general equilibrium model on the same footing as any other commodity and renders the entire system homogeneous.

In his writings on monetary reform, Walras focused his attention upon the questions, then current, of bimetallism and bank note issue. His work Théorie mathématique du bimétalUsme (1881) presented, in the form of an ad hoc model, a complete theory of the bimetallist standard with a fixed ratio. Basing his proposal on this model, as well as on his utility theory and his conception of “justice,” he advocated a symmetallist system in the form of a gold standard with a regulatory silver token currency. The state would regulate the quantity of a special silver token currency in such a way as to counteract the long wave fluctuations in the value of money. In the matter of bank note issue, Walras maintained that any system that fell short of 100 per cent metallic coverage was dangerous.

These arduous labors exhausted Walras. By 1892 he felt he could no longer go on with his teaching. The inheritance he received from his mother in that year enabled him to purchase an annuity and repay his old debts, incurred mainly in the publication and free distribution of his books and economic papers. Thereupon, he retired from the university on a pension of 800 francs a year and was succeeded in his chair by his protégé Vilfredo Pareto. He did not, however, lay down his pen. In the decade 1892-1902, as has been seen, he made some of his most important innovations in the theory of capital and money. He could not, however, find strength to write the systematic treatises he had planned on applied economics and social economics. Instead, he published two volumes of collected papers, Études d’économie sociale in 1896 and Études d’économie politique appliquée in 1898. From 1902 on, after completing his notes for what ultimately became the definitive edition of 1926, he devoted himself to puttering and to propaganda in favor of his theory. Upon the death of his second wife in 1900, her annuity ceased, and Walras and his unmarried daughter, Aline, moved, without regrets, to a modest apartment at Clarens, near Montreux, where he died on January 5, 1910. Six months before his death, the University of Lausanne celebrated his jubilee as an economist, on which occasion he was acclaimed in messages from all over the world as the founder of the general equilibrium school.

Though Walras had received occasional marks of recognition before his death, it was only posthumously that his reputation and influence grew to their present proportions. After 1910, Etienne Antonelli championed the Walrasian model in his lectures and writings in France. Elsewhere, Walras’ model has been the subject of continued emendations, controversy, and fluctuating evaluations. His crabbed notations have been streamlined; his crude mathematics polished, perfected, and modernized; his utility theory superseded by a theory of ordinal preference unencumbered by assumptions of cardinal measurement and independence; his production theory freed from implications that had left the distinction between free and scarce goods empirically hazy; his production functions generalized to admit more easily of variable coefficients of production; his investment theory disrassociated from postulates of certainty of outcome; and his unwarranted premise that equality between the number of unknowns and the number of independent equations is sufficient for a determinate solution supplanted by rigorous existence theorems. For all that, the main lines of the Walrasian model remain intact, and its authority is such that in 1949 Milton Friedman was forced to admit, “We curtsy to Marshall, but we walk with Walras” (p. 489). Some critics, while conceding the aesthetic qualities of the general equilibrium model, hold it to be sterile, little realizing that pure economics is no more intended for direct application to practical problems than pure mechanics is intended for guidance to machinists. Besides, it is putting a strange construction upon the word “sterility” to apply it to an over-all theory that is the acknowledged forebear of input-output analysis and that directly begot the modern conceptions of exchange, production, saving, investment, interest, and money and fitted them neatly into a single, coherent framework. This was the achievement of Walras, a lonely, cantankerous savant, often in straitened circumstances, plagued with hypochondria and a paranoid temperament, plodding doggedly through hostile, uncharted territory to discover a fresh vantage point from which subsequent generations of economists could set out to make their own discoveries.

William JaffÉ

[Directly related is the entryEconomicEquilibrium. See also the biographies ofBarone; BÖhm-bAwerk; Gossen; Jevons; Menger; Pareto; Wlcksell; Schlesinger.]

WORKS BY WALRAS

1860 L’économie politique et la justice. Paris: No publisher given.

1868 Recherche de l’idéal social: Lecons publiques faites à Paris. Paris: Guillaumin.

1874 Principle d’une théorie mathématique de l’échange. Académie des Sciences Morales et Politiques, Paris, Seances et travaux 101:97-116.

(1874-1877) 1954 Elements of Pure Economics: Or, the Theory of Social Wealth. Translated by William Jaffé. Homewood, 111.: Irwin; London: Allen & Unwin. → First published in French as Éléments d’économie politique pure. The definitive French edition appeared in 1926.

1881 Théorie mathématique du bimétallisme. Paris: Guillaumin.

1883 Théorie mathématique de la richesse sociale. Lausanne: Corbaz.

1886 Théorie de la monnaie. Lausanne: Corbaz.

(1896) 1936 Études d’économie sociale (Théorie de la repartition de la richesse sociale). 2d ed. Lausanne: Rouge.

(1898) 1936 Études d’économie politique appliquée (Théorie de la production de la richesse sociale). 2d ed. Lausanne: Rouge.

(1899) 1954 The Mechanism and Equations of Circulation and Money; Solution of the Equations of Circulation and Money; the Law of the Establishment and Variation of the Price of Money; Price Curve of the Money Commodity. Pages 315-337 in Léon Walras, Éléments of Pure Economics: Or, the Theory of Social Wealth. Homewood, 111.: Irwin; London: Allen & Unwin. → First published as Équations de la circulation, a paper read to the Société Vaudoise des Sciences Naturelles, and incorporated into the fourth edition of the Eléments in 1900.

The Correspondence of Léon Walras and Related Papers. 3 vols. Selected and edited by William Jaffé. Amsterdam: North Holland Publishing, 1965. → Contains letters dated 1857 to 1909.

SUPPLEMENTARY BIBLIOGRAPHY

Barone Enrico (1894)1936 Sul trattamento di quistioni dinamiche. Volume 1, pages 77-114 in Enrico Barone, he opere economiche. Bologna: Zanichelli. → First published in Volume 9 of the Giornale degli economisti, Series 2.

Boson Marcel 1951 Léon Walras, fondateur de la politique économique scientifique. Paris: Librairie Générale de Droit et de Jurisprudence.

Bousquet, G. H. 1964 L’autobibliographie inedite de Léon Walras (1906). Revue economique[1964]:295-304.

Friedman Milton 1949 The Marshallian Demand Curve. Journal of Political Economy 57:463-495. → Reprinted in Friedman’s Essays in Positive Economics (1953).

Hicks, J. R. 1934 Léon Walras. Econometrica 2:338-348.

Isnard Achille nicholas 1781 Traits des richesses, contenant I’analyse de I’usage des richesses en général et de leurs valeurs. 2 vols. London and Lausanne: Grasset.

JaffÉ, William 1935 Unpublished Papers and Letters of Léon Walras. Journal of Political Economy 43:187-207.

JaffÉ William 1967 Walras’ Theory of Tatonnement: A Critique of Recent Interpretations. Journal of Political Economy 75:1-19.

Jevons, W. Stanley (1871) 1879 The Theory of Political Economy. 5th ed. New York: Kelley. Pages xi-lii contain the preface to the second edition.

Kuenne, Robert E. 1963 The Theory of General Economic Equilibrium. Princeton Univ. Press.

Marget Arthur W. 1931 Léon Walras and the “Cash-balance Approach” to the Problem of the Value of Money. Journal of Political Economy 39:569-600.

Marget Arthur W. 1935 The Monetary Aspects of the Walrasian System. Journal of Political Economy 43: 145-186.

Patinkin Don (1956) 1965 Walras’ Theory of Tatonnement; Walras’ Theory of Money. Pages 531-540 and 541-572 in Don Patinkin, Money, Interest and Prices: An Integration of Monetary and Value Theory. 2d ed. New York: Harper.

Poinsot, Louis (1803) 1842 Éléments de statique. 8th ed., rev. & enl., with corrections. Paris: Bachelier. → An English translation was published in 1847 as The Éléments of Statics.

Schumpeter, Joseph A. (1910) 1951 Marie Esprit Léon Walras, 1834-1910. Pages 74-79 in Joseph A. Schumpeter, Ten Great Economists From Marx to Keynes. New York: Oxford Univ. Press. → First published in Zeitschrift fur Volkswirtschaft Sozialpolitik und Ver-waltung.

Schumpeter Joseph A. (1954) 1960 History of Economic Analysis. Edited by E. B. Schumpeter. New York: Oxford Univ. Press.

Walras Auguste 1831 De la nature de la richesse, et de I’origine de la valeur. Paris: Johanneau.

Wicksteed Philip H. (1894) 1932 An Essay on the Co-ordination of the Laws of Distribution. Series of Reprints of Scarce Tracts in Economic and Political Science, No. 12. London School of Economics and Political Science.

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Walras, Léon

Walras, Léon 18341910

BIBLIOGRAPHY

Marie Esprit Walras was born on December 16, 1834, in évreux (Upper Normandy, France) to Auguste (1801 1866) and Louise-Aline Sainte-Beuve (18111893). Despite having no university degree, Léon Walras was offered a professorship at the University of Lausanne on November 12, 1870. He officially occupied the chair of political economy from October 20, 1871 to 1892, when he retired early for health reasons. His political and social economy is best examined through the trilogy of works titled Éléments déconomie politique pure (Elements of Pure Economics or the Theory of Social Wealth, 18741877, 1889, 1896, 1900), Études déconomie sociale (Studies in Social Economics or the Theory of Distribution of Social Wealth, 1896), and Études déconomie politique appliquée (Studies in Applied Economics or the Theory of Production of Social Wealth, 1898). Walras died at his home in Clarens (Vaud, Switzerland) on January 5, 1910.

Founder of the School of Lausanne, Walras is one of the economists whose contributions have decisively influenced the development of economic theory. Almost simultaneously with, but independently from, Carl Menger (18401921) and Stanley Jevons (18351882), Walras introduced the concept of marginal utility (rareté ) and took an important step toward the mathematization of economics. In his view, mathematics is not only one of the possible forms of expressing economics but also is the form necessarily required for a rigorous formulation of economic laws.

However, Walrass most original and important contribution is the analysis of price determination by means of the interactions between the various markets that make up an economy. The modern analysis of the existence, uniqueness, and stability of general equilibrium had been inspired by Walrass Pure Economics. In the 1950s modern theorists, with the use of advanced mathematics, specified the hypotheses enabling them to rigorously prove the existence of a price system equalizing supply and demand on each marketthat is, the existence of a general equilibrium. In this perspective, the Walrasian tâtonnement (groping) was interpreted as a process of convergence of prices towards equilibrium, a representation of how markets actually work. Nevertheless, in the early 1970s enthusiasm chilled. It was proven that in a general equilibrium framework aggregate excess demand functions have an arbitrary nature, while specific assumption must be made to obtain uniqueness and stability results. To simplify matters rather drastically, as every change in the price system affects ones income and purchasing power, the aggregate excess demand functions that result behave capriciously. In others words, income effects prevent the groping process from leading to equilibrium. So, the correspondence between the hypothesis of the homo oeconomicus and the convergence towards equilibrium does not hold, and the tâtonnement process cannot be interpreted as the process that allows economic equilibrium to be reached.

Modern developments of general equilibrium have been inspired by Walrass theory of value in exchange (pure economics), while his theories of production and distribution of social wealth (applied and social economics) have been neglected. But from the perspective of the history of economic thought it is not possible to assert that pure economics is separable from the other two parts of the Walrasian triptych (applied economics and social economics) or that pure economics only is worthy of scientific consideration. Thanks to the publication of Walrass collected writings (19872005), historians of economic thought now rarely discuss Walrass works referring only to pure economics, even though there is still no consensus on the relationships between these three components of Walrass political and social economy.

Nevertheless, the actual and fundamental controversy about Walrass writings involves the meaning of general equilibrium theory and what it is supposed to refer to. Most scholars considered Walrass general equilibrium theory as an attempt to represent the actual working of nineteenth-century capitalism, even though they disagreed on its heuristic value. For most critics, the general equilibrium theory is simply inadequate for this task, both in Walrass and in modern versions. Others instead find in Walrass writing some elements pertinent for the understanding of real markets. Finally, some argue that one can learn more from the differences between model and reality than from their alleged similarities.

However, if one takes Walrass philosophy of science seriously, a different point of view emerges: general equilibrium does not refer to actual market working or other economic facts but to the social wealth considered in itself. Pure economics does not aim at representing, in a more or less faithful and simplified manner, the contingent reality but rather at grasping the essence of the reality which does not yet completely exist, a reality in its becoming. For Walras, general equilibrium is the perfect, ideal form, towards which economic systems are evolving but are not yet realized. This ideal form is described in Walrass Elements of Pure Economics, but in his other writings he often referred to the economic and social phenomena that were right before his eyes: one might cite the essays on money and credit, monopolies, and railroads, but also on salaries, tax system, and real estate. These studies are definitely far from being an apology of the market as a self-driven and self-regulating mechanism. Instead, they represent a long list of cases requiring State intervention. The State has to organize the economy in order to approach the ideal form represented by general equilibrium but it is also destined to produce as a monopolist where too much competition kills competition.

Finally, three different Léon Walras have to be considered. The first is a neoclassical icon, the founder of neowalrasian economics, but known by economists at best as the author of Elements of Pure Economics only. The second is the founder of the School of Lausanne and the father of general equilibrium as a formalized invisible hand. The third, unknown to economists and only recently discovered by historians of thought, is a critic not only of the capitalism of his time, but of market economy in itself.

SEE ALSO Economics, Neoclassical; Equilibrium in Economics; General Equilibrium; Lausanne, School of; Marginalism; Mathematical Economics; Stability in Economics ; Tâtonnement; Walras Law

BIBLIOGRAPHY

Jaffé, William, ed. 1965. Correspondence of Léon Walras and Related Papers. 3 vols. Amsterdam: North Holland.

Walras, Léon. 19872005. Auguste et Léon Walras: Œuvres Économiques Complètes. Vols. 514, ed. Pierre Dockès, Pierre-Henri Goutte, Claude Hébert, Claude Mouchot, Jean-Pierre Potier, and Jean-Michel Servet. Paris: Economica.

Roberto Baranzini

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neo-classical economics

neo-classical economics Economics, as an academic discipline, is predominantly the study of the allocation of scarce resources to alternative uses via market prices. The dominant paradigm in modern economics is neo-classical theory which developed from the so-called marginalist revolution pioneered by Leon Walras, William Stanley Jevons, and Alfred Marshall in the late nineteenth century. This posits that prices are determined by marginal utility (of consumers) and marginal productivity (of factors of production). Neo-classical theories are based on simple behavioural models at the micro-level (households, firms) which assume perfect information, freedom of movement, individual choice, optimizing and rational decision-making. The basic conditions for these models are private enterprise, consumer sovereignty, and market-clearing prices. Institutional influences on individual behaviour are defined exogenously as given characteristics and do not form part of the basic behavioural model. However, game-theoretic approaches have been developed recently to explain individual behaviour within institutional rules.

A recent development in modern economic theory, developed in the USA, goes under the name of ‘political economy’ and has nothing to do with radical or Marxist versions to which the label is more commonly applied. This literature applies neo-classical principles to areas outside the economy, such as public policy, focusing on artificially induced scarcities (‘rents’) which are produced by political pressure exerted by economic interest groups.

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Walras, Léon

Léon Walras, 1834–1910, French economist. After abandoning his studies in mining engineering, he became a freelance journalist, advancing the causes of economic and social reform. He later became a professor of political economy at the Univ. of Lausanne (1870–1892). One of the most influential of economists, Walras advanced several theories that served as the foundation of modern economic analysis. He is widely regarded as the founder of the theory of general economic equilibrium, mathematical economics, the concept of "imperfect competition," and the marginal utility theory. A prolific and creative writer, Walras's work also extended to such themes as managed currency, production, credit, and capital formation.

See his correspondence, ed. by W. Jaffé (3 vol., 1965), and Elements of Pure Economics (tr., 1984). See also D. A. Walker, ed., William Jaffe's Essays on Walras (1983).

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