Marie-Esprit-Léon Walras (; 16 December 1834 – 5 January 1910) was a French mathematical economist and

Georgist Georgism, also called in modern times Geoism, and known historically as the single tax movement, is an economic ideology holding that, although people should own the value they produce themselves, the economic rent derived from land—including ...

. He formulated the

marginal theory of value Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...

(independently of

William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...

and Carl Menger) and pioneered the development of

general equilibrium theory In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an ov ...

. Walras is best known for his book ''Éléments d'économie politique pure'', a work that has contributed greatly to the mathematization of economics through the concept of general equilibrium. The definition of the role of the entrepreneur found in it was also taken up and amplified by

Joseph Schumpeter Joseph Alois Schumpeter (; February 8, 1883 – January 8, 1950) was an Austrian-born political economist. He served briefly as Finance Minister of German-Austria in 1919. In 1932, he emigrated to the United States to become a professor at H ...

. For Walras, exchanges only take place after a Walrasian '' tâtonnement'' (French for "trial and error"), guided by the auctioneer, has made it possible to reach market equilibrium. It was the general equilibrium obtained from a single hypothesis, rarity, that led Joseph Schumpeter to consider him "the greatest of all economists". The notion of general equilibrium was very quickly adopted by major economists such as

Vilfredo Pareto Vilfredo Federico Damaso Pareto ( , , , ; born Wilfried Fritz Pareto; 15 July 1848 – 19 August 1923) was an Italian polymath (civil engineer, sociologist, economist, political scientist, and philosopher). He made several important contribut ...

Knut Wicksell Johan Gustaf Knut Wicksell (December 20, 1851 – May 3, 1926) was a leading Swedish economist of the Stockholm school. His economic contributions would influence both the Keynesian and Austrian schools of economic thought. He was married to th ...

and Gustav Cassel.

John Hicks Sir John Richards Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economic ...

and

Paul Samuelson Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "h ...

used the Walrasian contribution in the elaboration of the neoclassical synthesis. For their part, Kenneth Arrow and Gérard Debreu, from the perspective of a logician and a mathematician, determined the conditions necessary for equilibrium.

Biography

Walras was the son of a French school administrator

Auguste Walras Auguste Walras (; 1801–1866) was a French school administrator and economist. He was the father of Léon Walras, who was deeply influenced by his father's view on economics. Auguste Walras convinced his son to give up his original literary asp ...

. His father was not a professional economist, yet his economic thinking had a profound effect on his son. He found the value of goods by setting their scarcity relative to human wants. Walras enrolled in the

École des Mines de Paris Mines Paris - PSL, officially École nationale supérieure des mines de Paris (until May 2022 Mines ParisTech, also known as École des mines de Paris, ENSMP, Mines de Paris, les Mines, or Paris School of Mines), is a French grande école and a c ...

, but grew tired of engineering. He worked as a bank manager, journalist, romantic novelist and railway clerk before turning to economics.''

Economyths ''Economyths'' is a book by the mathematician David Orrell about the problems with mainstream economics, written for the general reader. The book was initially published in 2010 by Icon Books in the UK with the subtitle ''Ten Ways That Economics ...

'' (2010) by

David Orrell David John Orrell (born 1962 in Edmonton) is a Canadian writer and mathematician. He received his doctorate in mathematics from the University of Oxford. His work in the prediction of complex systems such as the weather, genetics and the economy ha ...

, p. 54 Walras received an appointment as the professor of political economy at the University of Lausanne. Walras also inherited his father's interest in

social reform A reform movement or reformism is a type of social movement that aims to bring a social or also a political system closer to the community's ideal. A reform movement is distinguished from more radical social movements such as revolutionary move ...

. Much like the

Fabians The Fabian Society is a British socialist organisation whose purpose is to advance the principles of social democracy and democratic socialism via gradualist and reformist effort in democracies, rather than by revolutionary overthrow. The Fab ...

, Walras called for the

nationalization Nationalization (nationalisation in British English) is the process of transforming privately-owned assets into public assets by bringing them under the public ownership of a national government or state. Nationalization usually refers to pri ...

of land, believing that land's productivity would always increase and that rents from that land would be sufficient to support the nation without taxes. He also asserts that all other taxes (i.e. on goods, labor, capital) eventually realize effects exactly identical to a

consumption tax A consumption tax is a tax levied on consumption spending on goods and services. The tax base of such a tax is the money spent on Consumption (economics), consumption. Consumption taxes are usually indirect, such as a sales tax or a value-added ta ...

, so they can hurt the economy (unlike a land tax). Another of Walras's influences was Augustin Cournot, a former schoolmate of his father. Through Cournot, Walras came under the influence of

rationalism In philosophy, rationalism is the epistemological view that "regards reason as the chief source and test of knowledge" or "any view appealing to reason as a source of knowledge or justification".Lacey, A.R. (1996), ''A Dictionary of Philosophy' ...

and was introduced to the use of mathematics in economics. As Professor of

Political Economy Political economy is the study of how Macroeconomics, economic systems (e.g. Marketplace, markets and Economy, national economies) and Politics, political systems (e.g. law, Institution, institutions, government) are linked. Widely studied ph ...

at the

University of Lausanne The University of Lausanne (UNIL; french: links=no, Université de Lausanne) in Lausanne, Switzerland was founded in 1537 as a school of Protestant theology, before being made a university in 1890. The university is the second oldest in Switzer ...

, Walras is credited with founding the

Lausanne school The Lausanne School of economics, sometimes referred to as the Mathematical School, refers to the neoclassical economics school of thought surrounding Léon Walras and Vilfredo Pareto. It is named after the University of Lausanne, at which both Walr ...

of economics, along with his successor

. Because most of Walras's publications were only available in French, many economists were unfamiliar with his work. This changed in 1954 with the publication of William Jaffé's English translation of Walras's ''Éléments d'économie politique pure''. Walras's work was also too mathematically complex for many contemporary readers of his time. On the other hand, it has a great insight into the market process under idealized conditions so it has been far more read in the modern era. Although Walras came to be regarded as one of the three leaders of the

marginalist Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...

revolution, he was not familiar with the two other leading figures of marginalism,

and Carl Menger, and developed his theories independently. ''Elements'' has Walras disagreeing with Jevons on the applicability, while the findings adopted by Carl Menger, he says, are completely in alignment with the ideas present in the book (even though expressed non-mathematically).

Life and career

General equilibrium theory

In 1874 and 1877 Walras published ''Éléments d'économie politique pure'' (1899, 4th ed.; 1926, éd. définitive), in English, ''Elements of Pure Economics'' (1954), trans. William Jaffé. That work that led him to be considered the father of the

. The problem that Walras set out to solve was one presented by

A. A. Cournot Antoine Augustin Cournot (; 28 August 180131 March 1877) was a French philosopher and mathematician who also contributed to the development of economics. Biography Antoine Augustin Cournot was born at Gray, Haute-Saône. In 1821 he entered o ...

, that even though it could be demonstrated that prices would equate

supply and demand In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...

to clear individual markets, it was unclear that an equilibrium existed for all markets simultaneously.

Walras's law Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the ''values'' of excess demand (or, conversely, excess market supplies) must sum to zero regardless of whether the prices are general equilibr ...

implies that the sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium. This implies that if positive excess demand exists in one market, negative excess demand must exist in some other market. Thus, if all markets but one are in equilibrium, then that last market must also be in equilibrium. While teaching at the Lausanne Academy, Walras began constructing a mathematical model that assumes a "regime of perfectly free competition", in which productive factors, products, and prices automatically adjust in equilibrium. Walras began with the theory of exchange in 1873 and then he proceeded to map out his theories of production, capitalization and money in his first edition. His theory of exchange began with an expansion of Cournot's demand curve to include more than two commodities, also realizing the value of the quantity sold must equal the quantity purchased thus the ratio of prices must be equal to the inverse ratio of quantities. Walras then drew a supply curve from the demand curve and set equilibrium prices at the intersection. His model could now determine prices of commodities but only the relative price. In order to deduce the absolute price, Walras could choose one price to serve as a unit of account, coined by Walras as the numeraire and state all other prices in units of this commodity. The term numeraire, meaning unit of account, has become part of the international vocabulary of economics and for many economists, the only French word they know. Using this numeraire he determined that marginal utility, or rarete, divided by the price must be equal for all commodities. Walras felt that because the value of what an individual consumer consumes is equal to the value of that individual's stock of goods, that the aggregate, the value of total sales must equal the value of total purchase, must hold true. This became known as Walras' Law which held that equilibrium equations can be derived from the others until only m-1 equations in the m-1 relative prices remain. Walras then expanded the theory to include production with the assumption of an existence of fixed coefficients in said production making possible a generalization that the marginal productivity of the factors of production varied with the amount of input, making factor substitution possible. Walras constructed his basic theory of general equilibrium by beginning with simple equations and then increasing the complexity in the next equations. He began with a two-person bartering system, then moved on to the derivation of downward-sloping consumer demands. Next he moved on to exchanges involving multiple parties, and finally ended with credit and money. Walras wrote down four sets of equations—one representing the quantity of goods demanded, one relating the prices of goods to their costs of production, one for the quantities of inputs supplied, and one showing the quantities of inputs demanded. There are four sets of variables to solve for, namely, the price of each good, the quantity of each good sold, the price of each factor of production, and the quantity of each of those factor bought by businesses. To simplify matters, Walras added one further equation to his model, requiring that all the money received must be spent, one way or the other. But there are now more equations than unknowns. From the theory of equations, one learns that a necessary but insufficient condition for the existence of a unique solution to a system of equations is that the number of equations must equal the number of variables. Walras tackled this problem by selecting an arbitrary good, G1, whose price is designated as the standard against which the prices of the other goods shall be compared. The system of equations can now be solved for the prices of all goods in terms of G1, though not for the absolute price levels.Pressman, Steven. ''Fifty Major Economists''. "Léon Walras (1834-1910)." 2nd ed., Routledge, 2006. The crucial step in the argument was

which states that any particular market must be in equilibrium, if all other markets in an economy are also in equilibrium. Walras's law hinges on the mathematical notion that excess market demands (or, inversely, excess market supplies) must sum to zero. This means that, in an economy with n markets, it is sufficient to solve n-1 simultaneous equations for market clearing. Taking one good as the

numéraire The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradables are expressed. In a monetary economy, actin ...

in terms of which prices are specified, the economy has n-1 prices that can be determined by the equation, so an equilibrium should exist. Although Walras set out the framework for thinking about the existence of equilibrium clearly and precisely his attempt to demonstrate existence by counting the number of equations and variables was severely flawed: it is easy to see that not all pairs of equations in two variables have solutions. A more rigorous version of the argument was developed independently by

Lionel McKenzie Lionel Wilfred McKenzie (January 26, 1919 – October 12, 2010) was an American economist. He was the Wilson Professor Emeritus of Economics at the University of Rochester. He was born in Montezuma, Georgia. He completed undergraduate studies at ...

and the pair

Kenneth Arrow Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economics ...

and

Gérard Debreu Gérard Debreu (; 4 July 1921 – 31 December 2004) was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize ...

in the 1950s. A significant part of the general equilibrium theory as introduced by Walras has become known as the

Walrasian auction A Walrasian auction, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across ...

which is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand. Walras suggests that equilibrium will be achieved through a process of ''tâtonnement'' (French for "trial and error"), a form of incremental hill climbing.

Economic value definition of utility

Léon Walras provides a definition of economic utility based on economic value as opposed to an ethical theory of value:

I state that things are useful as soon as they may serve whatever usage, as soon as they match whatever need and allow its fulfillment. Thus, there is here no point to deal with 'nuances' by way of which one classes, in the language of everyday conversation, utility beside what is pleasant and between the necessary and the superfluous. Necessary, useful, pleasant and superfluous, all of this is, for us, more or less useful. There is here as well no need to take into account the morality or immorality of the need that the useful things matches and permits to fulfill. Whether a substance is searched for by a doctor to heal an ill person, or by an assassin to poison his family, this is an important question from other points of view, albeit totally indifferent from ours. The substance is useful, for us, in both cases, and may well be more useful in the second case than in the first one.

In economic theories of value, the term "value" is unrelated to any notions of value used in ethics, they are homonyms.

Legacy

In 1941

George Stigler George Joseph Stigler (; January 17, 1911 – December 1, 1991) was an American economist. He was the 1982 laureate in Nobel Memorial Prize in Economic Sciences and is considered a key leader of the Chicago school of economics. Early life and ...

wrote about Walras: What caused the re-appraisal of Walras's consideration in the US, was the influx of German-speaking scientists – the German version of the ''Éléments'' was published in 1881. According to

Schumpeter Joseph Alois Schumpeter (; February 8, 1883 – January 8, 1950) was an Austrian-born political economist. He served briefly as Finance Minister of German-Austria in 1919. In 1932, he emigrated to the United States to become a professor at Ha ...

Major works

''Éléments d'Économie Politique Pure''

The ''Éléments'' of 1874/1877 are the work by which Léon Walras is best known. The full title is * Éléments d'Économie Politique Pure, ou Théorie de la richesse sociale. The

half title One half ( : halves) is the irreducible fraction resulting from dividing one by two or the fraction resulting from dividing any number by its double. Multiplication by one half is equivalent to division by two, or "halving"; conversely, ...

page uses only the title ('Éléments d'Économie Politique Pure') whereas inside the body (e.g. p. 1 and the contents page) the subtitle ('Théorie de la richesse sociale') is used as if it were the title.

Plan of work

The work was issued in two instalments (''fascicules'') in separate years. It was intended as the first of three parts of a systematic treatise as follows: * 1^re partie:– Éléments d'Économie Politique Pure, ou Théorie de la richesse sociale. ** Section I. Objet et divisions de l'économie politique et sociale. ** Section II. Théorie mathématique de l'échange. ** Section III. Du numéraire et de la monnaie. ** Section IV. Théorie naturelle de la production et de la conommation de la richesse. ** Section V. Conditions et conséquences du progrès économique. ** Section VI. Effets naturels et nécessaires des divers modes d'organisation économique de la société. * 2^e partie:– Éléments d'Économie Politique Appliquée, ou Théorie de la production agricole, industrielle et commerciale de la richesse. * 3^e partie:– Éléments d'Économie Sociale, ou Théorie de la répartition de la richesse par la propriété et l'impôt. Works with titles echoing those proposed for Parts II and III were published in 1898 and 1896. They are included in the list of other works below.

Editions

* ''First'' (1874/1877). Most readily available. Described by Walker and van Daal as a 'brilliant expression of pure originality, containing many theoretical innovations' which 'needed alteration and development in a variety of important respects'. * ''Second'' (1889). Revised, corrected and enlarged. * ''Third'' (1896). A minor revision with new appendices. This is considered the best edition by Walker and van Daal. * ''Fourth'' (1900). Revised and extended. According to Walker and van Daal, 'these changes resulted in an incomplete, internally contradictory, and occasionally incoherent text'. * ''Fifth'' (1926). Posthumous; published by his daughter Aline. 'Édition définitive, revue et augmentée'. Follows the fourth.

Derived work

The 'Théorie Mathématique de la Richesse Sociale' included in the list of other works (below) is described by the National Library of Australia as 'a series of lectures and articles that together summarize the mathematical elements of the author's ''Élements'' '.Catalogue record at https://catalogue.nla.gov.au/Record/2018624.

English Translations

* William Jaffé (1954) of the ''fifth'' edition as ''Elements of Pure Economics''. * Donald A. Walker and Jan van Daal (2014) of the ''third'' edition as ''Elements of Theoretical Economics''. Walker and van Daal describe Jaffé's translation of the word ''crieur'' as 'a momentous error that has misled generations of readers'.

Online and facsimile editions

* Online: * Facsimile: cheap photographic reprints are produced by . Both of these are made from the ''first'' edition and are defective in respect of illustrations. The original figures were included as folding plates (presumably at the end of each ''fascicule''). The online edition contains only Figs. 3, 4, 10, and 12 whereas the facsimile contains only Figs. 5 and 6.

Other works

* ''Francis Saveur'', 1858. * "De la propriété intellectuelle", 1859, ''Journal des économistes''. * * "Paradoxes économiques I", 1860, ''Journal des économistes''. * "Théorie critique de l'impôt", 1861. * ''De l'impôt dans le Canton de Vaud'', 1861. * * "La bourse et le crédit", 1867, ''Paris Guide''. * * "Correspondance entre M. Jevons, professeur a Manchester, et M. Walras, professeur a Lausanne", 1874, ''Journal des économistes''. * * "Un nuovo ramo della matematica. Dell' applicazione delle matematiche all' economia politica", 1876, ''Giornale degli economisti''. * ''Théorie mathématique de la richesse sociale'', 1883. * "Notice autobiographique de Léon Walras", 1893. * ''Études d'économie sociale; Théorie de la répartition de la richesse sociale'', 1896. * ''Études d'économie politique appliquée; Théorie de la production de la richesse sociale'', 1898. * "Théorie du crédit", 1898, ''Revue d'économie politique''. * "Sur les équations de la circulation", 1899, ''Giornale degli economisti'' * "Cournot et l'Économique Mathématique", 1905, ''Gazette de Lausanne''. * "La Paix par la Justice Sociale et le Libre Échange", 1907, ''Questions Pratiques de Legislation Ouvrière''. * ''L'état et le chemin de fer'' (1875). * "Leone Walras, Autobiografia", 1908, ''Giornale degli Economist''i. * "Un initiateur en économie politique, A.A. Walras", 1908, ''La Revue du Mois''. * "Économique et méchanique", 1909, ''Bulletin de la Société Vaudoise de Sciences Naturelles'' * ''Correspondence of Léon Walras and related papers'' (ed. by William Jaffé, 3 vols.), 1965.

Note

References

External links

Biography and major works
* {{DEFAULTSORT:Walras, Leon Mines ParisTech alumni 1834 births 1910 deaths People from Évreux General equilibrium theorists 19th-century French economists 20th-century French economists University of Lausanne faculty Georgist economists Neoclassical economists