Very often, people seem to confuse Say’s Law (or the closely related Walras’ Law) for the proposition that nominal spending doesn’t matter, or that aggregate demand shortfalls and excesses cannot occur. As I shall demonstrate, however, its clear implication is the opposite when one considers the case of money as a tradable good.
Imagine an economy in which money and goods are exchanged for each other. (Multiple different types of money can exist, although this does not change the outcome.) Many of the trades made involve money being traded for other goods. However, money is still “supplied” and “demanded” in the same sense that any other good is, and has a “price” in terms of other goods. Thus, there exist states of monetary equilibrium and disequilibrium.
Monetary disequilibrium exists when, at a given real value of the monetary unit, the the real quantity of money the public demands to hold (and is willing to purchase by selling other goods to obtain money) is not equal to the real quantity of money actually provided. As Walras’ Law implies, a shortage or surplus of money is matched by a surplus or shortage (respectively) in all other goods collectively, as measured by the market value of said surpluses and shortages.
So what, then, does monetary disequilibrium imply in terms of nominal spending? When a surplus of money is held (in real terms), there exists a shortage of other goods to be bought with money, and the public seeks to reduce its real holdings of money by increasing nominal spending of held money on goods. Such a situation is that of an excess of aggregate demand.
Conversely, when a shortage of money is held (in real terms), there exists a surplus of other goods to be bought with money, and the public seeks to increase its real holdings of money by decreasing nominal spending of held money on goods. Such a situation is that of an aggregate demand shortfall.
Walras’ and Say’s Laws concern themselves with markets in equilibrium and disequilibrium, and the fact that a shortage of good A in terms of some other good B it is traded for implies that there also exists a surplus of the good B in terms of good A. One need not reject this insight to accommodate the empirical existence of shortfalls and excesses of nominal spending. One must only consider what it is that is actually being spent.