Walras' law
From Wikipedia, the free encyclopedia
Walras’ Law is a principle in general equilibrium theory that states that if every market but the last market are in equilibrium, then the last market must also be in equilibrium. Walras’ Law is named for the French economist Leon Walras, although it was first expressed by John Stuart Mill in Essays on Some Unsettled Questions of Political Economy (1844).
Contents |
[edit] Quick Definitions:
- A market for a particular commodity in in equilibrium if demand for that commodity equals supply, given the market price of the commodity. For example, suppose the market price of cherries is $0.15. If a farmer is willing to sell 50 cherries at $0.15 each, and his neighbors are willing to buy 50 cherries at $0.15, then there is no shortage or excess of cherries in the system and the market clears. The market for cherries is in equilibrium.
- An economy is in general equilibrium if the market for every commodity in the economy is in equilibrium. Not only does the market for cherries clear, but so do the markets for apples, oranges, labor, and any other commodities in the economy.
- Excess Demand refers to the extra units of a commodity that are demanded, over and above the supply of that commodity, when the market is not in equilibrium. This is also known as a shortage. The case of negative excess demand is known as a surplus.
[edit] Walras' Law
The sum of excess demand of all markets will equal zero, whether or not the economy is in equilibrium.
This implies that if there is positive excess demand in one market, there will be negative excess demand in another. Furthermore, if we know that all markets but one are in equilibrium, then the last market must also be in equilibrium.
This last implication is often applied in formal general equilibrium models. In particular, in order 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 indeed 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. If there is no excess demand for cherries, then by Walras' Law, there is no excess demand for apples either. If there is excess demand for cherries, then there will be negative excess demand (excess supply) 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 can be viewed as an implication of every agent's budget constraint holding with equality. An agent's budget constraint is an equation stating that the total market value of the agent's planned purchases of commodities must equal the total market value of the agent's planned sales of commodities (including sales of financial assets such as 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 purchases of all commodities must equal the total market value of all agents' planned sales of all commodities. It follows that the market value of total excess demand in the economy must be zero, which is a statement of Walras' Law.
[edit] Implications
[edit] Labor market
Because of Walras' Law, if all goods markets are in equilibrium, the market for labor will also be in equilibrium. This is contrary to the Keynesian school of thought, which allows for disequilibrium in labor, even when all other markets are in equilibrium.
