Walras' law
Encyclopedia
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, conversely, excess market supplies) must sum to zero. That is, Σ XD = Σ XS = 0. Walras' Law is named for the 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).
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 be less than or equal to 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.
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 contradicts 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,
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...
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
Economic shortage
Economic shortage is a term describing a disparity between the amount demanded for a product or service and the amount supplied in a market. Specifically, a shortage occurs when there is excess demand; therefore, it is the opposite of a surplus....
(or, conversely, excess market supplies) must sum to zero. That is, Σ XD = Σ XS = 0. Walras' Law is named for the economist Leon Walras
Léon Walras
Marie-Esprit-Léon Walras was a French mathematical economist associated with the creation of the general equilibrium theory.-Life and career:...
, who taught at the University of Lausanne
University of Lausanne
The University of Lausanne in Lausanne, Switzerland was founded in 1537 as a school of theology, before being made a university in 1890. Today about 12,000 students and 2200 researchers study and work at the university...
, although the concept was expressed earlier but in a less mathematically rigorous fashion by John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...
in his Essays on Some Unsettled Questions of Political Economy
Essays on Some Unsettled Questions of Political Economy
Essays on Some Unsettled Questions of Political Economy is a treatise on political economics by John Stuart Mill. Walras' law, a principle in general equilibrium theory named in honour of Léon Walras, was first expressed by Mill in this treatise....
(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 shortagesEconomic shortageEconomic shortage is a term describing a disparity between the amount demanded for a product or service and the amount supplied in a market. Specifically, a shortage occurs when there is excess demand; therefore, it is the opposite of a surplus....
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 clearMarket clearingIn economics, market clearing refers to either# a simplifying assumption made by the new classical school that markets always go to where the quantity supplied equals the quantity demanded; or# the process of getting there via price adjustment....
, 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. 'Excess demand' may be used more generally to refer to the algebraic value of quantity demanded minus quantity supplied, whether positive or negative.
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 be less than or equal to 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.
Labor market
Neoclassical macroeconomic reasoningNeoclassical economics
Neoclassical economics is a term variously used for approaches to economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand, often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits...
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 contradicts the Keynesian
Keynesian economics
Keynesian economics is a school of macroeconomic thought based on the ideas of 20th-century English economist John Maynard Keynes.Keynesian economics argues that private sector decisions sometimes lead to inefficient macroeconomic outcomes and, therefore, advocates active policy responses by the...
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
Liquidity trap
A liquidity trap is a situation described in Keynesian economics in which injections of cash into an economy by a central bank fail to lower interest rates and hence to stimulate economic growth. A liquidity trap is caused when people hoard cash because they expect an adverse event such as...
for money) that permits an excess supply of labor and consequently, temporary involuntary unemployment, even if markets for goods are in equilibrium,