Léon Walras

Marie-Esprit-Léon Walras was a French mathematical economist and Georgist. He formulated the marginal theory of value and pioneered the development of general equilibrium theory.


Walras was the son of a French school administrator Auguste Walras. 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, but grew tired of engineering. He worked as a bank manager, journalist, romantic novelist and railway clerk before turning to economics. 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. Much like the Fabians, Walras called for the nationalization 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 eventually realize effects exactly identical to a consumption tax, so they can hurt the economy.
Another of Walras's influences was Augustin Cournot, a former schoolmate of his father. Through Cournot, Walras came under the influence of French rationalism and was introduced to the use of mathematics in economics.
As Professor of Political Economy at the University of Lausanne, Walras is credited with founding the Lausanne school of economics, along with his successor Vilfredo Pareto.
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 revolution,
he was not familiar with the two other leading figures of marginalism, William Stanley Jevons 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.

Life and career

General equilibrium theory

In 1874 and 1877 Walras published Éléments d'économie politique pure, in English, Elements of Pure Economics, trans. William Jaffé.
That work that led him to be considered the father of the general equilibrium theory. The problem that Walras set out to solve was one presented by A. A. Cournot, that even though it could be demonstrated that prices would equate supply and demand to clear individual markets, it was unclear that an equilibrium existed for all markets simultaneously. Walras's law 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.
The crucial step in the argument was Walras's law 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 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 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 and the pair Kenneth Arrow and Gérard Debreu in the 1950s.
A significant part of the general equilibrium theory as introduced by Walras has become known as the Walrasian auction 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, 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 a 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.


In 1941 George Stigler 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:

Major works

Éléments d'Économie Politique Pure

The Éléments of 1874/1877 are the work by which Walras is best known. The full title is
The half title page uses only the title whereas inside the body the subtitle is used as if it were the title.

Plan of work

The work was issued in two instalments in separate years. It was intended as the first of three parts of a systematic treatise as follows:
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.


The ‘Théorie Mathématique de la Richesse Sociale’ included in the list of other works 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 ’.


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

Both of these are made from the first edition and are defective in respect of illustrations. The original figures were included as folding plates. The online edition contains only Figs. 3, 4, 10, and 12 whereas the facsimile contains only Figs. 5 and 6.

Other works

« Je dis que les choses sont utiles dès qu'elles peuvent servir à un usage quelconque, dès qu'elles répondent à un besoin quelconque et en permettent la satisfaction. Ainsi, il n'y a pas à s'occuper ici des nuances par lesquelles on classe, dans le langage de la conversation courante, l'utilité à côté de l'agréable entre le nécessaire et le superflu. Nécessaire, utile, agréable et superflu, tout cela, pour nous, est plus ou moins utile. Il n'y a pas davantage à tenir compte ici de la moralité ou de l'immoralité du besoin auquel répond la chose utile et qu'elle permet de satisfaire. Qu'une substance soit recherchée par un médecin pour guérir un malade ou pour un assassin pour empoisonner sa famille, c'est une question très importante à d'autres points de vue, mais tout à fait indifférente au nôtre. La substance est utile, pour nous, dans les deux cas, et peut l'être plus dans le second que dans le premier. » Elements d'économie pure, ou théorie de la richesse sociale, 1874