



. 




Fish 




Coconuts 




Bananas 




Summation 




In a barter world, buying cannot be done unless one sells at the same time, and selling cannot be done unless one buys at the same time. In a world of barter, the only way one can finance purchases is by selling, and there is no reason to sell except to finance purchases. It is for this reason that Say's Law implies that a column should sum to zero. The act of supplying is also an act of demanding; supply creates its own demand.
The table contains the plans of Friday and Saturday in addition to Crusoe. Notice that adding each of their columns results in a total of zero. If, however, rows are added, there is no need to sum to zero, and the rows for fish and bananas do not sum to zero. A nonzero total here means that plans will not be realized (work out). The +2 in the fish row indicates that at the original prices there will be an oversupply or surplus of fish. The 2 in the banana row means that at the original prices there will be an overdemand or a shortage of bananas. To make the markets clear, the price of fish should fall and the price of bananas should rise. In turn, the new prices will affect future plans. Most economists (but certainly not all) have believed that, with repeated changes in prices and plans, eventually an equilibrium situation will be reached so that all rows will sum to zerothat quantity supplied will equal quantity demanded in each market.
The logic of the table implies that there can be no general glut or oversupply of goods, which was the point Say and others were arguing. It is possible for "gluts" of particular goods, but counterbalancing this is a shortage or undersupply of other goods. It is not possible, given the assumption that columns must sum to zero, for an oversupply (or underdemand) of all goods to exist. This conclusion won the debate in the early 19th century and remained unchallenged until the 20th century.
The logic of the table also implies that if all markets except one are balanced, then the last one also must balance. This conclusion was named after Leon Walras and has become known as Walras' Law. (Say's Law captured in a verbal and intuitive way the spirit of general equilibrium analysis.) Walras' Law says that if a system has n markets, and n1 of them are in equilibrium, then the final n^{th} market must also be in equilibrium. This conclusion is widely used in macroeconomics (because it says we can ignore a market), and we will appeal to it in later discussions to justify conclusions.
However, Say's Law has problems when we leave the world of barter.