The Quantity Theory and the Balanced Budget Theorem
Let us temporarily make the simplifying assumption that the marginal propensity to spend out of income is unity. Although, as will be shown below, this assumption is not necessary for the quantity theory, it is a classic quantity theory case. Armed with this assumption, consider a case where the government has the same income velocity as the private economy. In this case the balanced budget multiplier is zero: the government is merely substituting itself for private firms or households in the income-expenditure chain. On the other hand, assume that the government's marginal Marshallian k is zero, i.e., that the government holds no additional cash balances when tax receipts and expenditures rise by the same amount. In this case, we have the classical balanced budget multiplier of unity. This is because the government's expenditure raises income by an equal amount without reducing private expenditures at all. Third, the government's k may be greater than zero, but less than that of the private economy. In this case the balanced budget multiplier is greater than zero, but less than unity. This is the case recently considered by Selden.1 Finally, the government's k may be greater than the private k, and if so, the balanced budget multiplier is negative.2 How do these quantity theory balanced budget multipliers look from the viewpoint of Keynesian theory? It turns out that Keynesian theory is not able to handle these cases, for if the marginal propensity to consume (the Keynesian analogue of the marginal propensity to spend) is unity, there is no equilibrium income level to be computed by multiplier theory. To apply this specifically to the balanced budget theorem, consider what happens to both of its proofs if the marginal propensity to consume is unity. The first proof, which is to compare the tax and expenditure chains, then looks as follows: