# Léon Walras : biography

**Léon Walras** ( December 16, 1834 – January 5, 1910) was a French mathematical economist. He formulated the marginal theory of value (independently of William Stanley Jevons and Carl Menger) and pioneered the development of general equilibrium theory.

## Notes

## Life and career

Walras, whose full name was Marie Esprit Leon Walras, was the son of French economist Auguste Walras. His father was a school administrator and 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 Paris School of Mines,Economyths (2010) by David Orrell, page 54 but grew tired of engineering. He also tried careers as a bank manager, journalist, romantic novelist and a clerk at a railway company before turning to economics.Economyths (2010), by David Orrell, page 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. Much like the Fabians, Walras called for the nationalization of land, believing that land’s value would always increase and that rents from that land would be sufficient to support the nation without taxes.

Another of Walras’ 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.

Professor of Political Economy at the University of Lausanne,Economyths (2010) by David Orrell, page 54 Switzerland, Walras is credited for having founded what subsequently became known, under direction of his Italian disciple, the economist and sociologist Vilfredo Pareto, as the Lausanne school of economics.

Because for a long time most of Walras’ publications were only available in French, only a relatively small section of the economics profession really became familiar with his work. This changed in the 1950s, largely due to the work of William Jaffé, the translator of Walras’ main works, and the editor of his *Complete Correspondence* (1965). Walras’ 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.

### Marginalist theory

Although Walras came to be regarded as one of the three leaders of the marginalist revolution,Sandmo, Agnar (2011). Economics Evolving: A history of economic thought, Princeton University Press: Princeton, p. 190 he was not familiar with the two other leading figures of marginalism, William Stanley Jevons and Carl Menger, and developed his theories independently.

### General equilibrium theory

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. The problem that Walras set out to solve was one presented by 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 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 created a system of simultaneous equations in an attempt to solve Cournot’s problem "(which supposedly Walras at first thought was complete merely because the number of equations equalled the number of unknowns)"

The crucial step in the argument was Walras’ Law which states that any particular market must be in equilibrium, if all other markets in an economy are also in equilibrium. Walras’ 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 numeraire 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 by Kenneth Arrow and Gérard Debreu in the 1950s.