Knowledge that Transforms

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:

Henry D. Lytton, Public Sector Productivity in the Truman-Eisenhower Years: A Springboard for the Kennedy Administration?, The Review of Economics and Statistics, Vol. 43, No. 2 (May, 1961), pp. 182-184

HIS paper presents a model of T which is an extension to n sectors of the original one-sector equilibrium paths developed by R. F. Harrod and E. D. Domar.1 Following Harrod, we employ discrete periods of time and hence a (first-order) difference equation technique. However, in order to give the model a prescriptive rather than a predictive overtone, the first differences refer to the immediate future instead of the immediate past. In addition, an allowance for depreciation is included in the model. By balanced growth we simply mean the existence of equilibrium (the equality of supply and demand) in every market in every time period. Equiproportionate of each market is a special case of as used in this paper. Prices do not explicitly enter the model. Supply in each market is an increasing linear function of the existing capital stock in that sector or industry, and hence the model refers to a one-factor economy. However, capital is not transferable from one sector to another. The single factor of production (capital) is produced by a single industry, the investment-goods industry, the input into which is also capital. Demand for the output of each industry, with the exception of the investment-goods sector, is an increasing linear function of net real income. By definition, these industries are producers of consumption goods, all of which are non-inferior from the point of view of the income-demand relation. The demand for investment goods is a mixed accelerator-multiplier relation. The solution of the system expresses net aggregate output as a function of integral values of time. The output of each sector at any time can then be determined from the structural equations of the model.

T HE object of this paper is to demonstrate that it is exceedingly difficult, if not impossible, to develop a theory of the business cycle on the basis of a simple multiplier-accelerator model. Such theories have experienced considerable popularity during the postwar years, even though it can be shown that they do not constitute internally consistent systems useful in describing the economic instability encountered in capitalistic economies. The particular cycle models under discussion here assume a relatively high capital-output coefficient which implies an excessive degree of income instability. To avoid unrealistically high or low levels of income, exogenous ceilings and floors are introduced into the model which limit income changes in either direction. Here it will be demonstrated that the subsidiary assumption of floors and ceilings represents a curiously round-about method of avoiding most implications of the assumption of the fixed capital-output ratio which underlies the whole model. It is necessary to substitute a more flexible production function for the postulated constant accelerator in order to avoid these unrealistic implications within a fairly simple theoretical model. The nonlinear accelerator model, which was developed by Hicks and Goodwin, is probably the most sophisticated model built upon the interaction of constant multiplier and acceleration coefficients.' Here we shall use the Hicks model as an example. Already in his review of Harrod's Towards a Dynamic Economics, Hicks presented an outline of his later theory and stated what he conceived to be the central problem of a theory of economic instability: