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# Walras

[val-ra]
Walras, Léon, 1834-1910, French economist. After abandoning his studies in mining engineering, he became a free-lance journalist, advancing the causes of economic and social reform. He later became a professor of political economy at the Univ. of Lausanne (1870-1892). One of the most influential of economists, Walras advanced several theories that served as the foundation of modern economic analysis. He is widely regarded as the founder of the theory of general economic equilibrium, mathematical economics, the concept of "imperfect competition," and the marginal utility theory. A prolific and creative writer, Walras's work also extended to such themes as managed currency, production, credit, and capital formation.

See his correspondence, ed. by W. Jaffé (3 vol., 1965), and Elements of Pure Economics (tr., 1984). See also D. A. Walker, ed., William Jaffe's Essays on Walras (1983).

Walras’ Law is a principle in general equilibrium theory asserting that when considering any particular market, if all other markets in an economy are in equilibrium, then that specific market must also be in equilibrium. Walras’ Law hinges on the mathematical notion that excess market demands (or, inversely, excess market supplies) must sum to zero. That is, ΣXD = ΣXS = 0. Walras' Law is named for the mathematically inclined economist Leon Walras, who taught at the University of Lausanne, although the concept was expressed earlier but in a less mathematically rigorous fashion by John Stuart Mill in his Essays on Some Unsettled Questions of Political Economy (1844).

## Definitions

• A market for a particular commodity is in equilibrium if, at the current price of the commodity, the quantity of the commodity demanded by potential buyers equals the quantity supplied by potential sellers. For example, suppose the current market price of cherries is \$1 per pound. If all cherry farmers summed together are willing to sell a total of 500 pounds of cherries per week at \$1 per pound, and if all potential customers summed together are willing to buy 500 pounds of cherries in total per week when faced with a price of \$1 per pound, then the market for cherries is in equilibrium because neither shortages nor surpluses of cherries exist.
• An economy is in general equilibrium if every market in the economy is in equilibrium. Not only must the market for cherries clear, but so too must all markets for all commodities (apples, automobiles, etc.) and for all resources (labor and economic capital) and for all financial assets, including stocks, bonds, and money.
• Excess Demand refers to a situation in which a market is not in equilibrium at a specific price because the number of units of an item demanded exceeds the quantity of that item supplied at that specific price. Excess demand yields an economic shortage. A negative excess demand is synonymous with an excess supply, in which case there will be an economic surplus of the good or resource.

## Walras' Law

Walras' Law implies that the sum 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.

This last implication is often applied in formal general equilibrium models. In particular, to characterize general equilibrium in a model with m agents and n commodities, a modeler may impose market clearing for n - 1 commodities and "drop the n-th market-clearing condition." In this case, the modeler should include the budget constraints of all m agents (with equality), as well as any additional equations (such as first-order conditions) characterizing agents' optimal behavior. Imposing the budget constraints for all m agents ensures that Walras' Law holds, rendering the n-th market-clearing condition redundant.

In the farmer example, suppose that the only commodities in the economy are cherries and apples, and that no other markets exist. If excess demand for cherries is zero, then by Walras' Law, excess demand for apples is also zero. If there is excess demand for cherries, then there will be a surplus (excess supply, or negative excess demand) for apples; and the market value of the excess demand for cherries will equal the market value of the excess supply of apples.

Walras' Law is ensured if every agent's budget constraint holds with equality. An agent's budget constraint is an equation stating that the total market value of the agent's planned expenditures, including saving for future consumption, must equal the total market value of the agent's expected revenue, including sales of financial assets such as bonds or money. When an agent's budget constraint holds with equality, the agent neither plans to acquire goods for free (e.g., by stealing), nor does the agent plan to give away any goods for free. If every agent's budget constraint holds with equality, then the total market value of all agents' planned outlays for all commodities (including saving, which represents future purchases) must equal the total market value of all agents' planned sales of all commodities and assets. It follows that the market value of total excess demand in the economy must be zero, which is an implication of Walras' Law.

## Implications

### Labor market

Neoclassical macroeconomic reasoning tends to ignore financial markets and consequently concludes that because of Walras' Law, if all markets for goods are in equilibrium, the market for labor must also be in equilibrium. Thus, by neoclassical reasoning, Walras' Law refutes the Keynesian conclusion that negative excess demand and consequently, involuntary unemployment, may exist in the labor market, even when all markets for goods are in equilibrium. The Keynesian rebuttal is that this neoclassical perspective ignores financial markets, which may experience excess demand (e.g., a Keynesian liquidity trap for money) that permits an excess supply of labor and consequently, temporary involuntary unemployment, even if markets for goods are in equilibrium,