|Died||5 January 1910 75) (aged|
Clarens, now part of Montreux, Switzerland
|Field|| Economics |
| Lausanne School |
|Alma mater||École des Mines de Paris|
|Contributions|| Marginal utility |
Marie-Esprit-Léon Walras (French: [valʁas] ; 16 December 1834 – 5 January 1910) was a French mathematical economist and Georgist. He formulated the marginal theory of value (independently of William Stanley Jevons and Carl Menger) 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 (i.e. on goods, labor, capital) eventually realize effects exactly identical to a consumption tax,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 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 (even though expressed non-mathematically).
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 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 (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 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 (French for "trial and error"), a form of incremental hill climbing.
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 Stiglerwrote about Walras:
There is no general history of economic thought in English which devotes more than passing reference to his work. … This sort of empty fame in English-speaking countries is of course attributable in large part to Walras's use of his mother tongue, French, and his depressing array of mathematical formulas.
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.[ citation needed ] According to Schumpeter:
Walras is … greatest of all economists. His system of economic equilibrium, uniting, as it does, the quality of 'revolutionary' creativeness with the quality of classic synthesis, is the only work by an economist that will stand comparison with the achievements of theoretical physics.
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 (‘Éléments d'Économie Politique Pure’) whereas inside the body (eg. p. 1 and the contents page) the subtitle (‘Théorie de la richesse sociale’) is used as if it were the title.
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:
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 (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 ’.
Walker and van Daal describe Jaffé’s translation of the word crieur as ‘a momentous error that has misled generations of readers’.
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.
Neoclassical economics is an approach to economics focusing on the determination of goods, outputs, and income distributions in markets through supply and demand. This determination is often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits by firms facing production costs and employing available information and factors of production, in accordance with rational choice theory, a theory that has come under considerable question in recent years.
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 overall general equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which only analyzes single markets.
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and quantity is called the "competitive quantity" or market clearing quantity. But the concept of equilibrium in economics also applies to imperfectly competitive markets, where it takes the form of a Nash equilibrium.
Jean Charles Léonard de Sismondi, whose real name was Simonde, was a historian and political economist, who is best known for his works on French and Italian history, and his economic ideas. His Nouveaux principes d'économie politique, ou de la richesse dans ses rapports avec la population (1819) represents the first liberal critique of laissez-faire economics. He was one of the pioneering advocates of unemployment insurance, sickness benefits, a progressive tax, regulation of working hours, and a pension scheme. He was also the first to coin the term proletariat to refer to the working class created under capitalism, and his discussion of mieux value anticipates the Marxist concept of surplus value. According to Gareth Stedman Jones, "much of what Sismondi wrote became part of the standard repertoire of socialist criticism of modern industry."
Maurice Félix Charles Allais was a French physicist and economist, the 1988 winner of the Nobel Memorial Prize in Economic Sciences "for his pioneering contributions to the theory of markets and efficient utilization of resources", for Maurice Allais contribution, along with John Hicks and Paul Samuelson, to neoclassical synthesis. They formalize the self-regulation of markets, that Keynes refuted, while reiterating some of his ideas.
In economics and commerce, the Bertrand paradox — named after its creator, Joseph Bertrand — describes a situation in which two players (firms) reach a state of Nash equilibrium where both firms charge a price equal to marginal cost ("MC"). The paradox is that in models such as Cournot competition, an increase in the number of firms is associated with a convergence of prices to marginal costs. In these alternative models of oligopoly, a small number of firms earn positive profits by charging prices above cost. Suppose two firms, A and B, sell a homogeneous commodity, each with the same cost of production and distribution, so that customers choose the product solely on the basis of price. It follows that demand is infinitely price-elastic. Neither A nor B will set a higher price than the other because doing so would yield the entire market to their rival. If they set the same price, the companies will share both the market and profits.
In economics, an Edgeworth box is a graphical representation of a market with just two commodities, X and Y, and two consumers. The dimensions of the box are the total quantities Ωx and Ωy of the two goods.
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies. Wassily Leontief (1906–1999) is credited with developing this type of analysis and earned the Nobel Prize in Economics for his development of this model.
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at the prices set. The model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot's book Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838) in which Cournot had put forward the Cournot model. Cournot argued that when firms choose quantities, the equilibrium outcome involves firms pricing above marginal cost and hence the competitive price. In his review, Bertrand argued that if firms chose prices rather than quantities, then the competitive outcome would occur with price equal to marginal cost. The model was not formalized by Bertrand: however, the idea was developed into a mathematical model by Francis Ysidro Edgeworth in 1889.
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 all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand.
The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel, and Hugo F. Sonnenschein in the 1970s. It states that the excess demand curve for a market populated with utility-maximizing rational agents can take the shape of any function that is continuous, has homogeneity degree zero, and is in accordance with Walras's law. This implies that market processes will not necessarily reach a unique and stable equilibrium point.
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 Walras and Pareto held professorships. Polish economist Leon Winiarski is also said to have been a member of the Lausanne School.
Charles Gide was a French economist and historian of economic thought. He was a professor at the University of Bordeaux, at Montpellier, at Université de Paris and finally at Collège de France. His nephew was the author André Gide.
Auguste Walras was a French school administrator and (amateur) economist. He was the father of Léon Walras, who was deeply influenced by his father's view on economics.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. By convention, these applied methods are beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
The progressive theory of capital is an economic theory posited by Léon Walras in 1874 in part 5 of his book Elements of Pure Economics.
In economics, utility is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a good or service is the change in the utility from an increase in the consumption of that good or service.
Michael Allingham is a British economist whose main work has been on equilibrium theory, choice theory, and distributive justice.
In microeconomics, an excess demand function is a function expressing excess demand for a product—the excess of quantity demanded over quantity supplied—in terms of the product's price and possibly other determinants. It is the product's demand function minus its supply function. In a pure exchange economy, the excess demand is the sum of all agents' demands minus the sum of all agents' initial endowments.
Joseph-Clément Garnier was a French economist and politician. He was a prolific author and a member of many learned societies. In the last years of his life he was a Senator for Alpes-Maritimes.
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