Léon Walras

Walras

Marie-Esprit-Léon Walras (December 16, 1834 in Évreux, France - January 5, 1910 in Clarens, near Montreux, Switzerland) was a French economist, considered by Joseph Schumpeter as "the greatest of all economists". He was a mathematical economist associated with the creation of the general equilibrium theory.

Biography

He was born 1834 as the son of the French proto-marginalist economist and schoolteacher, Auguste Walras. After spending a Bohemian youth in Paris as a novelist and art critic, Leon Walras soon followed his father's footsteps on almost every count: 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, the mathematization of economics). After spending some unfruitful years in the cooperatives movement, Walras was appointed to 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).

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. The last decade of Walras's life was spent in frustrated loneliness, bitter at the neglect of his work, incapacitated by senility and mental illness. He died in 1910.

Walras’ work

Walras’ criticism of laissez-faire system

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 economic system’s functioning.

The prime objective of Walras's 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…..”, he asked, “……..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.

In 1874 and 1877 Walras published Elements of Pure Economics, a work that led him to be considered the father of the general equilibrium theory. Walras set out his Elements in a methodology that can be briefly summarized in three distinct parts: Walras Indentity, Walras Equilibrium and Walras Law.

Walras Identity: first step towards general equilibrium

It deals with some aspects of Walras' theory - the use of mathematics in economics, the notion of free competition, the notion of utility, and price formation in competitive markets. Walras provides his definition of the scope of economics, subjective value theory and the mathematical method.

He starts with dsiscussing two-commodity pure exchange where demand and supply are derived from utility-maximization; his 'auctioneer' and the tatonnement process of 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 ).

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

Walras equilibrium

Then, towards the synthetizing these aspects into the equilibrium models, he introduces multi-market pure exchange; counts 'equations and unknowns' to find existence; considers multi-market tatonnement 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. The activities of households, firms and industries could not be understood in isolation from one another or when detached from the economy as a whole.

Walras Law

There are two major implications of Walras Identity ( and/or Equilibirum ) discussed in the above paragraphs. As indicated by our derivation, Walras Identity is valid whether or not market prices equate demand with supply for each individual commodity. It has, however, two very important implications:

One implication relates to the 'generality' of equilibrium. The other refers to states of dis-equilibrium.

To recapitulate verbally, we have shown that if all but one of the markets in an economy are in equilibrium, then that other market also must be in equilibrium. In the next section we shall see what Walras Identity implies when at least one market is in disequilibrium. This implication 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 labour 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 we now look 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. This is Walras Law.

What is important for macroeconomic modelling 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. As we shall see, 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 modeller says "let us assume that all markets are in equilibrium except the labour market" ( University of Melbourne 2000 ).

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 (e.g. 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 (e.g. 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". They would say, "either all markets are in equilibrium, or more than one is in disequilibrium, but we can't have 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 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 thus reducing (and eventually removing entirely) the excess supply in the labor market.

As a consequence of the above, 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 and therefore as wrong or 'bad' in theory and so inadmissible.

The attack on the relevance of Walras Law for modelling situations in which there is involuntary unemployment was developed by several economists 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 ) will get started (Leijonhufvud, 1981).

Walras’ legacy

Leon Walras transformed economics from a literary discipline into a mathematical, deterministic science. For the first time, Walras expressed rigorously 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 "tatonnement". This conception of economics led to important new insights about the stability of markets and about the capitalist economic system.

His work laid the foundation for mathematical economics and led the historian of economic thought Joseph Schumpeter to call the system of equations set out in Walras’ Elements "the Magna Charta of Economics” ( Schumpeter 1954 ).

References

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• Leijonhufvud, A., “Keynes and the Classics: Two Lectures Institute of Economic Affairs”, London, 1969, reprinted in: A Leijonhufvud, Information and Coordination Oxford University Press, New York, 1981
• Schumpeter, J., History of Economic Analysis, George Allen and Unwin, London,1954, Schumpeter, 1954, p. 242
• University of Melbourne, Department of Economics, 20 June 2000

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

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