Knowledge that Transforms

These two formulations are different from each other except that a constant H happens to be a Samuelson optimal value. In other words, Strotz's optimization is more constrained than Samuelson's, and Strotz's optimization cannot achieve Pareto optima except in the special case just mentioned.2 Does this difference between the two approaches invalidate Strotz's propositions in section II and section III in his article? If we confine our problem to Pareto optima, Strotz's propositions happen to be meaningful, that is, when H happens to be Samuelson's optimal value. And even in this case the relation between the optimal value of H and Pareto optima is ambiguous, and we must explicitly treat productive services of fixed income assets in the model. But it can be expected that such an approach would introduce complications into the model. Although Strotz's formulation has these difficulties, I believe, Samuelson's comment on Strotz's article, in the Appendix to Aspects of Public Expenditure Theories in this REVIEW, XL (November I958) is valid, that is, changing public goods does materially affect the distribution of income and all decisions have to be made simultaneously.

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.