Léon Walras

Léon Walras

Marie-Esprit-Léon Walras (December 16, 1834 – January 5, 1910) was a French economist. Although not influential in his lifetime, his contributions to economic theory later came to be studied and respected worldwide. Separately, but almost simultaneously with William Stanley Jevons and Carl Menger, Walras developed the idea of marginal utility, but his greatest contribution was in what is now called general equilibrium theory. Before Walras, economists had made little attempt to show how a whole economy, involving the buying and selling of multiple goods, fits together and reaches an equilibrium. Walras set out to do this, and although he did not succeed completely, he took the first major steps in developing mathematical economics, which enables one to understand market forces and to be better able to establish an economically stable human society, benefiting all people.



Marie-Esprit-Léon Walras was born in 1834, in Évreux, France, the son of the French proto-marginalist economist and schoolteacher, Auguste Walras.

After spending his youth in several careers—he was a student at the School of Mines for a year, worked in journalism, as a novelist, an art critic, and for several businesses—Walras eventually returned to the study and teaching of economics. Thus, Walras followed his father's footsteps: He adopted his father's socialist policy positions on taxation and land reform (in fact, he was a proponent of outright land nationalization) as well as his main ideas on economic theory (subjectivist theory of value and the mathematization of economics).

After spending some fruitless years in the cooperatives movement, Walras finally received an academic appointment at the Academy of Lausanne in 1870. It was there that he wrote and published the first edition of his magnum opus, the Elements of Pure Economics (1874). However, this location was not ideal. The dominant thinking in economics at the time was in Britain, and Walras' writings in French had no significant impact on the rest of the profession.

In 1893, Walras was succeeded in his chair by his young disciple, Vilfredo Pareto. The two men formed the core (and some argue the full extent) of what became known as the Lausanne School. He retired in 1892, at the age of 58.

The last decade of Walras's life was spent in frustrated loneliness, bitter at the neglect of his work, and incapacitated by dementia. He died in 1910, in Clarens, near Montreux, Switzerland.


Although several commentators had described the Walrasian perspective on the economic system as one in which "no blade of grass can move without altering the position of the stars," it has become the standard starting point for the economic profession to analyze the over-all functioning of an economic system.

In 1874 and 1877, Walras published Elements of Pure Economics, a work that provided the foundation of the general equilibrium theory. In this work, Walras provided his definition of the scope of economics. Major aspects of Walras' theory include the use of mathematics in economics, the notion of free competition, the notion of utility, and price formation in competitive markets.

His goal was to solve the problem presented by Cournot, namely that even though models had been developed that could explain the behavior of individual markets, it was still unknown how multiple goods interacted with each other to affect the supply and demand in multiple markets. This was a problem considered by Cournot to be one that "would surpass the powers of mathematical analysis."

Walras set out in his Elements a methodology that can be briefly summarized in three distinct parts: Walras Identity, Walras Equilibrium, and Walras Law.

Walras Identity

Walras starts by discussing two-commodity pure exchange, where demand and supply are derived from utility-maximization. His "auctioneer" and the tâtonnement process of reaching stability is introduced here.

As a first step toward demonstrating the possibility of a general equilibrium solution, Walras examined the case of the simplest economy imaginable. It possessed only two goods to be exchanged (identified as x and y). All persons were assumed to be buyers of one good or sellers of the other. On these assumptions, it could be argued that the supply of x and the demand for y (as well as vice versa) were interdependent because the market demand for y (or x) was derived from the incomes received by sellers of x (or y). Consistent with neo-classical procedure, it was, of course, assumed that the terms on which sellers were prepared to exchange were regulated by the marginal utilities of x and y. Through competitive bidding an equilibrium price ratio would be established (Walras, Elements 1874).

Walras envisioned tâtonnement (in English, "groping") as a trial-and-error process in which a price was called out and people in the market said how much they were willing to demand or supply at that price. If there was an excess of supply over demand, then the price would be lowered so that less would be supplied and more would be demanded. Thus prices would "grope" toward equilibrium. Walras assumed, highly unrealistically, that no actual exchanges were made until equilibrium was reached through this process.

This proposition is known as "Walras Identity." In words, it states that the money value of all planned market purchases when added together is equal to the aggregate money value of all planned market sales.

Walras Equilibrium

Then, to synthesize these aspects into the equilibrium model, Walras introduced multi-market pure exchange; counted "equations and unknowns" to find existence; and considered multi-market tâtonnement with an auctioneer:

The problem became more intricate, of course, when more than two goods were involved. In the three-commodity economy (with goods x, y, and z), three price ratios could be established (x:y, x:z, and y:z). One of these ratios, however, would be redundant, adding no information that could not be derived from the other two. This example illustrated a larger principle: Namely, that in a multi-good economy, the number of equilibrium price ratios required was always one less than the number of goods involved in exchange. Thus in an economy with n goods, (n-1) exchange ratios would have to be determined through competitive bidding. The redundant commodity could then be regarded as a standard—or a numeraire—in terms of which all other price ratios could be expressed. This standard commodity, whatever its identity, would possess all of the essential properties of money (Walras, Elements 1874).

This procedure also had an important recommendation in that it emphasized the interdependence of all prices within the economic system. At the same time, Walrasian general equilibrium dissolved the standard lines of demarcation between micro and macro-theory. According to his model, the activities of households, firms, and industries could not be understood in isolation from one another or detached from the economy as a whole.

Walras Law

There are two major implications of Walras Identity (and/or Equilibrium) discussed in the above paragraphs. As indicated, Walras Identity is valid whether or not market prices equate demand with supply for each individual commodity. This has two very important implications: One relates to the "generality" of equilibrium; the other refers to states of dis-equilibrium.

First, he showed that if all but one of the markets in an economy are in equilibrium, then that other market also must be in equilibrium. The implication of Walras Identity when at least one market is in disequilibrium is known as Walras Law.

In a Walrasian economic model (and in many others as well) each trader will plan to dispose one way or another of all of the income they intend to receive from selling goods, their labor services, financial assets, or whatever. Consequently, for each trader the total value of their planned supply must exactly equal the total value of their planned demands. If one looks at the relationship between aggregate value of all commodities demanded by all traders and the aggregate value of all commodities supplied by all traders, the two must be equal. This implies that, should there ever be an excess of demand over supply for any one commodity, there must be a corresponding excess supply over demand (an excess of supply over demand is also called "negative excess demand") for at least one other commodity, otherwise the aggregate value of amounts agents wish to supply could not be equal to the aggregate value of amounts agents wish to demand.

Another way to put this is to say that the sum of excess demands over all the markets in the economy must equal zero, and that this applies whether or not all markets are in (general) equilibrium. Thus, Walras Law states that

∑ S = ∑ D (where S is surplus; D is demand)

holds for ALL markets.

What is important for macroeconomic modeling is that Walras Law implies that if there is excess supply (negative excess demand) in one market, then there must, corresponding to this, be positive excess demand in at least one other market. This implication of Walras Law leads many to be concerned about the theoretical grounding of Keynes' theory of unemployment and to be worried when a macroeconomic modeler says, "let us assume that all markets are in equilibrium except the labor market."

Walras vs. Keynes

It is an implication of Walras Law that an excess supply in any one market must be "matched by" an "equivalent" excess demand elsewhere (for example, an excess demand for commodities) since the sum of excess demands in a market economy must be zero. This implies that if one market has excess demand there must be at least one other market with a corresponding level of excess supply. Secondly, the excess supply of labor must be accompanied by an offsetting excess demand elsewhere (for example, for commodities) because the unemployed workers must have been intending to do ("buy") something with the wages they hoped to earn. This would seem to be in conflict with the Keynesian claim that involuntary unemployment can be an "equilibrium"—and thus a persistent—state of affairs in a (free) market economy.

Thus, there are two reasons for imagining conflicts between Walras Law and Keynes' model of the economy.

First, followers of Walras would say that it does not make sense to assume that all markets are in equilibrium except the labor market. According to Walras Law, either all markets are in equilibrium, or more than one is in disequilibrium, but there cannot be a situation where only one market is in disequilibrium.

Second, they would say that involuntary unemployment cannot persist in a market economy with flexible wages and prices. They would argue that if the commodities market has excess demand, then the prices of commodities will tend to rise, and consequently this will tend to reduce the level of excess demand in that market. In the labor market, where there is excess supply, they would assert that the money wage will tend to fall. The joint effect of the rising price level together with a falling money wage is that the real wage will tend to drop, and more workers will be hired, thus reducing (and eventually removing entirely) the excess supply in the labor market.

In this way, many would see the pronouncements of Keynes, that the economy could find itself with an excess supply of labor and yet, in all (other) respects be in "equilibrium," as being in conflict with Walras Law. Thus, Keynes' model involving unemployment is contradicted by Walras Law.

Several economists attacked the relevance of Walras Law for modeling situations in which there is involuntary unemployment, holding that Keynes must have had in mind that Walras Law was inapplicable to the problem he was studying. However, since they would measure excess demands and supplies as differences between planned (or notional) demands and supplies, and not actual (or "effective") demands and supplies, even Keynes maintained that there can be conditions under which excess demands (or supplies) will not be "effectively" communicated so that, although certain prices (including wages) are at disequilibrium levels, no process of bidding them away (from these inappropriate levels) can begin (Leijonhufvud, 1981).

Criticism of laissez-faire system

The prime objective of Walras' intellectual program was to produce an exhaustive account of the implications of a regime of perfect competition. Part of the value of this exercise, as he saw it, lay in the fact that many economists had been too readily persuaded of the merits of laissez-faire:

How could these economists prove that the results of free competition were beneficial and advantageous if they did not know just what these results were? … And how could they know these results when they had neither framed definitions nor formulated relevant laws to prove their point? …the fact that economists have often extended the principle of free competition beyond the limits of its true applicability is proof positive that the principle has not been demonstrated.

For his purposes, perfect competition was likened to a situation in which buyers and sellers could be brought together in a massive auction "in such a way that the terms of every exchange are openly announced and an opportunity is given to sellers to lower their prices and to buyers to raise their bids." These conditions were admittedly divorced from reality. He defended the procedure by asking: “What physicist would deliberately pick cloudy weather for astronomical observations instead of taking advantage of a cloudless night?” In his view, the case for a procedure which began with abstract general cases and took up the qualifications later was too self-evident to require further comment.


Léon Walras transformed economics from a literary discipline into a mathematical, deterministic science. Walras' work, for the first time, rigorously expressed the view that all markets are related, and that their relationships can be described and analyzed mathematically. These interrelated markets tend toward a "general equilibrium" position, undergoing a constant interactive adjustment process that Walras called a tâtonnement. This conception of economics led to important new insights about the stability of markets and the capitalist economic system.

Walras' work laid the foundation for mathematical economics, leading the historian of economic thought Joseph Schumpeter to describe him as "the greatest of all economists," and to call the system of equations set out in Walras’ Elements "the Magna Carta of Economics" (Schumpeter 1954).


  • Walras, Leon. 1859. "De la propriété intellectuelle" in Journal des Economistes.
  • Walras, Leon. 1860. L'économie politique et la justice; Examen critique et réfutation des doctrines économiques de M. P.J.. Produhon précédes d'une introduction à l'étude de la question sociale.
  • Walras, Leon. 1860. "Paradoxes économiques I" in Journal des Economistes.
  • Walras, Leon. 1861. Théorie critique de l'impôt.
  • Walras, Leon. 1874. "Correspondance entre M. Jevons, professeur a Manchester, et M. Walras, professeur a Lausanne" in Journal des economists.
  • Walras, Leon. 1874. Éléments d'économie politique pure, ou théorie de la richesse sociale (Elements of Pure Economics, or the theory of social wealth).
  • Walras, Leon. 1874. "Principe d'une théorie mathématique de l'échang" in Journal des Economistes.
  • Walras, Leon. 1876. Un nuovo ramo della matematica. Dell' applicazione delle matematiche all' economia poliitca, Giornale degli economisti.
  • Walras, Leon. 1883. Théorie mathématique de la richesse sociale.
  • Walras, Leon. 1889. Etudes d'économie politique appliquée; Théorie de la production de la richesse sociale.
  • Walras, Leon. 1898. "Théorie du credit" in Revue d'économie politique.
  • Walras, Leon. 1899. "Sur le equations de la circulations" in Giornale degli economisti.
  • Walras, Leon. 1905. "Cournot et l'Économique Mathématique" in Gazette de Lausanne.
  • Walras, Leon. 1908. "Un initiateur en économie politique" in A.A. Walras, La Revue du Mois.
  • Walras, Leon. 1909. "Économique et méchanique" in Bulletin de la Societe Vaudoise de Sciences Naturelles.


  • Leijonhufvud, A. 1981. Keynes and the Classics: Two Lectures Institute of Economic Affairs. London: Oxford University Press.
  • Schumpeter, J. 1954. History of Economic Analysis. London.
  • University of Melbourne. Walras Law and Macroeconomics. Retrieved May 1, 2008.

External links

All links retrieved September 19, 2016.


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