Walras' law

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Walras' Law, named for Leon Walras (a mathematical economist in the late 19th century) but first expressed by John Stuart Mill in Essays on Some Unsettled Questions of Political Economy (1844), is a principle in general equilibrium theory that states that if markets for all but one good are in equilibrium, then all markets must be in equilibrium and the economy is in general equilibrium.

First, we define equilibrium for a good to be the situation in which the price of the good is such that the supply of the good is equal to the demand of the good. To illustrate, if Farmer Bing has one hundred cherries, and at $0.15 a cherry he wants to sell 50 cherries and keep the rest, then $0.15 is an equilibrium price if the total number of cherries that all his neighbors are willing to buy at $0.15 is exactly 50.

Now, for more complicated economies where there is more than one good on the market, we define general equilibrium to be the situation in which all the prices are such that each good is in equilibrium. It is also important to remember that, even though most of the time people want an unlimited amount of anything, when talking about equilibrium we are talking about a situation in which no one would be willing to pay any more money (i.e., no one would want to give up more of another good) to get more of the good in question. Walras' law states that if all but one good is in equilibrium, then all the goods are in equilibrium and the economy is in general equilibrium.

The idea behind it is that at any time that one person wants more of one good, she must be willing to sell some of another good in order to get it. If this occurs, then it is two goods, not simply one, which are not in equilibrium. To illustrate, consider an economy in which Batman and Robin trade guns for butter. In this situation, money is only useful in order to buy or sell guns or butter. For simplicity, say Batman starts off with all the butter and Robin starts off with all the guns. So, assume the gun market is in equilibrium, i.e., Batman has purchased the exact amount of guns from Robin that Robin was willing to sell. The only way the butter market could be in disequilibrium is if Robin wants to purchase more or less butter than Batman is willing to sell. If Robin wants to buy more butter than Batman wants to sell, then it must mean that Robin is willing to sell guns in order to get butter, but that Batman is not interested in accepting those guns in exchange for butter. Thus, both guns and butter are out of equilibrium.

P'X(P)=0 P>=0 Where P is a price X is an amount vector in an economy with general equilibrium.

Walras' law says that there cannot be a one-sided disequilibrium in markets. For example, if the labour market is not in equilibrium because there is excess supply or in other words, unemployment, then there has to be a disequilibrium elsewhere that matches it, like excess demand in the goods market. In other words, total excess demand and supply across all markets balance each other out.

This is somewhat contrary to the Keynesian thinking that the labour market can be in disequilibrium in a general equilibrium model.

Another implication of Walras' law is that the budget constraint, properly defined, will be binding. This means that p*x=w in which p is a price vector, x is a vector of demands for various goods and w wealth.