Walras’ law is a powerful modeling tool that is used by economists when they undertake general equilibrium analysis. It captures the interdependence between markets implied by the budgetary constraint that all individual transactors (i.e., a single person, a household, a firm, or the government) must take into account when they formulate purchase and sales plans.
It is assumed that no individual transactor in a market economy is so misguided as to suppose that he or she can acquire something for nothing. This being the case, the plan to purchase (or sell) something necessarily implies the plan to sell (or purchase) something of equal value. In the language of economics, each individual must satisfy his or her budget constraint. Consequently, for each individual the total value of the planned supply must exactly equal the total value of the planned demand. This means that there can be neither an excess of demand over supply (excess demand) nor an excess of supply over demand (excess supply) at the level of the individual.
It follows by simple aggregation that there can be no excess demand or excess supply in the aggregate whether one is summing over the individuals as individuals or as participants in various markets, and this must be true whether or not prevailing market prices are such as to equate demand with supply for each specific commodity. In other words, the aggregate market value of supply equals the aggregate market value of demand for any set of prices, not just the equilibrium set of prices. This proposition sometimes is called Walras’ law but more commonly is known as Walras’ identity.
Walras’ identity implies that if there is ever an excess of demand over supply for any single commodity, there must be a corresponding excess of supply over demand for at least one other commodity; otherwise the aggregate value of commodities that agents wish to supply could not be equal to the aggregate value of commodities that agents wish to demand. Another way to put this is to say that the aggregate value of the excess demands and the excess supplies over all the markets must equal zero and that this applies whether or not all the markets are in equilibrium. This proposition is one of a number of logical implications of Walras’ identity that is given the name Walras’ law. Léon Walras explicitly formulated and drew upon this proposition in his attempt to explain how general economic equilibrium may be established in a market economy (Walras  1954).
Walras’ law is a statement that refers to all markets taken together (that is, it refers to the aggregation of the markets for final goods and services along with the markets for raw materials, labor, money, and bonds) and should not be confused with a proposition known as Say’s law, or at least one version of it (Sowell 1972), which claims that there never can be an excess supply of final goods and services taken alone. Although Walras’ law asserts the logical impossibility of oversupply in all markets taken together, it does not rule out the possibility of there being an oversupply in a particular market, such as the market for final goods and services, taken alone.
Walras’ identity and Walras’ law are valid whether or not market prices equate demand with supply for each and every commodity, and because of this they have implications for both equilibrium and disequilibrium situations. Those implications are of such fundamental importance in modeling interdependence between markets that they often have been used by writers to define Walras’ law.
Equilibrium in a market is a situation in which the price of the commodity is such that the supply of the commodity is equal to the demand for it. Now, suppose a set of prices has been established that will equate demand with supply in every market except the n th market. Because there can be neither excess supply nor excess demand in the aggregate, it follows that if all but one of the markets in an economy are in equilibrium, that other market also must be in equilibrium. Thus, to demonstrate that a situation of general equilibrium holds, it suffices to show that n – 1 markets are in equilibrium. This implication of Walras’ law plays an important role in models of markets and models of asset portfolios.
In regard to the implications of Walras’ law for disequilibrium, the law implies that regardless of the price that is set, the aggregate value of excess demands in the system equals the aggregate value of excess supplies. This carries the implication that an excess supply in any one market must be matched by an equal value of excess demand in some other market or markets. To put this statement slightly differently, if there is a disequilibrium in any one market, at least one other market must also be in disequilibrium.
This implication of Walras’ law leads many to be concerned about the theoretical grounding of John Maynard Keynes’s theory of unemployment, which seems to suggest that the labor market can be in disequilibrium even if all other markets are in equilibrium. An important contribution to this debate was made in 1965 by Robert Clower, who pointed out that in Walrasian analysis the excess demands and supplies are measured as differences between planned or “notional” demands and supplies, not between actual or “effective” demands and supplies. Clower suggested that Walrasian analysis is not appropriate for modeling situations in which there is involuntary unemployment (an excess supply of labor) because this excess supply in the labor market will result in household incomes that are lower than what the households were counting on when they formulated their expenditure plans. As a result the excess supply in the labor market will be matched by only a notional and not an effective excess demand for commodities.
Although in this situation certain prices will be at disequilibrium levels, no process of bidding them away from those inappropriate levels may get started, and so it can be argued that unemployment persists because the market signals that are presupposed in much general equilibrium analysis are not transmitted. Consideration of issues such as these has led to the development of non-Walrasian approaches to economics. In particular, in 1971 and 1976 Robert Barro and Herschel Grossman formalized the ideas of Clower and others and laid the foundations for a non-Walrasian macroeconomics.
SEE ALSO Barro-Grossman Model; Economics, New Classical; Economics, New Keynesian; General Equilibrium; Macroeconomics; Market Clearing; Prices ; Tâtonnement; Walras, Léon
Arrow, Kenneth J., and F. H. Hahn. 1971. General Competitive Analysis. San Francisco: Holden-Day.
Barro, Robert J., and Herschel I. Grossman. 1971. A General Disequilibrium Model of Income and Employment. American Economic Review 61 (1): 82–93.
Clower, Robert. 1965. The Keynesian Counter-Revolution: A Theoretical Appraisal. In The Theory of Interest Rates, eds. F. H. Hahn and F. P. R. Brechling, 103–125. London: Macmillan.
Patinkin, Don. 1987. Walras’ Law. In The New Palgrave: A Dictionary of Economics, vol. 4, eds. John Eatwell, Murray Milgate, and Peter Newman, 863–868. London: Macmillan.
Sowell, Thomas. 1972. Say’s Law: An Historical Analysis. Princeton, NJ: Princeton University Press.
Walras, Léon.  1954. Elements of Pure Economics. Trans. William Jaffe. London: Allen and Unwin.