"Say’s Law" is often defined as "supply creates its own demand." Furthermore, many authors fail to make the distinction between the "Classical" (as in the Classical Political Economy [CPE] Adam Smith and David Ricardo) and "Neoclassical" (as in the marginalist or demand-and-supply-equilibrium [DSE] theories of Marshall, Pigou, and modern ‘standard’ or ‘textbook’ microeconomics) versions of Say’s Law. Keynes himself lumped together Ricardo with Marshall and Pigou, including them all in what he wrongly termed ‘classical’ economics. What are the differences between the Classical and Neoclassical versions of Say’s Law?

The Classical version of Say’s Law is akin to what is known today as the national income accounting identity: production generates incomes sufficient to purchase that production. This is true by definition. But this certainly does not say that all production will necessarily be purchased. There is no mechanism in CPE that ensures all production will be bought. Unlike neoclassical economics, in CPE the interest rate does not serve as a mechanism that tends to equate savings and investment. There were some classical authors who believed that savings would tend to be invested, because in CPE the same social class of society—capitalists—made most of the decisions to both save and invest. But they had no theory that required that to be the case. Furthermore, there is nothing in CPE that says that the level of output will necessarily be the full employment level, or that there will be no unemployment.

In neoclassical economics, Say’s Law includes—but goes beyond—the statement of the national income accounting identity. In neoclassical economics there is a theory concerning how—under certain conditions (usually described as "perfect competition in all markets, including factor markets" or, what amounts to the same thing, "all prices—including factor prices—are perfectly flexible")—not only does production generate incomes sufficient to purchase that production, but all production will in fact be purchased. Furthermore, in neoclassical economics the same theory explains why the level of aggregate output will always tend to be the full employment level. Finally, and importantly, while the price mechanism in general is the key, the core of the neoclassical version of Say’s Law is the interest rate mechanism that will tend to equate aggregate savings and aggregate investment at the full employment level of output and income.

The Classical Political Economists divided economic society into three great classes, each receiving a particular kind of income: capitalists (profits), workers (wages), and landlords (rent). Let’s leave out the landlords for the moment, as well as government and foreign trade. We will also include for now the "classical assumption" that workers do not save (they spend all their income on consumption goods to live) and capitalists ‘live on air’ (they don’t consume). These are actually not that outrageous, since many lower income people do not earn enough to save (and if we leave out mortgages, most savings is business retained earnings), and while capitalists eat, their consumption does not go up and down with normal increases and decreases of profits.

Aggregate income must be equal to aggregate wages (the wage bill, W) plus aggregate profits, P:

Y = W + P (1)

Aggregate output is:

Y = C + I (2)

Since workers spend all their income on consumption and capitalists live on air:

W = C (3)

Therefore:

I = P (4)

In the aggregate, investment equals profits; profits are savings. In the Post Keynesian version of this model, causality goes from I => P. The Polish economist Michal Kalecki described the situation as "Capitalists get what they spend, and workers spend what they get." In the classics, the same social group made both investment and saving decisions.