A FEW years ago Professor Alvin H. Hansen IAJL developed a model sequence in which the multiplier analysis and the acceleration principle were combined. This was done by making increments to the national 1 consist of three parts: (I) governmental deficit spending in which each of the periodic expenditures by government was assumed to be of equal size; (2) induced private consumption expenditure the size of each of the successive induced consumption expenditures being determined by applying the marginal propensity to consume to the preceding period's increment to income; (3) induced private investment the size of each of the successive expenditures being determined by applying the coefficient of magnification (the acceleration principle, or relation) to the difference (positive or negative) between the induced consumption expenditure of any given period and that of the preceding period. As is well known, without the inclusion of the third component, the curve of national rises at a decreasing rate and approaches, as a limiting increment, the product of the multiplier and the constant increment to governmental contributions.2 Inclusion of a given coefficient of magnification, in conjunction with the first two factors, yields (for most relevant values of the multiplier and the coefficient of magnification) a curve of national which fluctuates about this limiting increment 3 as Professor Paul A. Samuelson has shown.4 Samuelson's generalization of Professor Hansen's model sequence covers a wide range of values for the marginal propensity to consume and the coefficient of magnification. This generalization proceeds on two assumptions: (i) increments to governmental deficit spending are of equal value for each successive period of expenditure; (2) in any given case, the marginal propensity to consume (a) and the coefficient of magnification (03) do not change in value, over time. Under these assumptions, Samuelson shows that the successive increments to national can be written: Yt = It + aYt-i + a,q (Y,-lY t-2), where Yt is the increment to national at time t, and where It is the governmental contribution at time t.5 This, of course, follows because the second and third terms are the equivalents, respectively, of induced consumption and induced investment. Samuelson's formula is sufficiently general to be applicable to cases in which autonomous investment (I t) is permitted to fluctuate over time, but his analysis is confined to the case in which It is constant; and, to my knowledge, no attention has ever been given to the interactions of a constant multiplier, a constant coefficient of magnification, and autonomous investment expenditures which vary in size over time; nor has the equally important case of cyclically fluctuating multipliers and magnification coefficients -a case which I shall treat in a later article received any attention. Such investi1 In studies of this sort it is, I believe, usually implicit that an increment to national income is defined as national at time t minus national at time 0, where national at time 0 is either zero or comprised entirely of Hansen's basic-income-level consumption (see pp. 289-92 of his Fiscal Policy and Business Cycles, New York, I94), and where national for each of the two periods preceding the initial period (time O) is equal to that of time 0; in short, an increment to national income has been implicitly defined, in economic literature, in such a manner that the national of time 0 does not contain any element of autonomous investment, induced investment, or induced consumption. The terminology and the charts of this paper are based upon this definition for an increment to national income, 'where incorme at time 0 is comprised entirely of basicincome-level consumption. However, as long as the national for each of the two periods preceding the initial period (time 0) is equal to that of time 0, we should get the same general results where the national of time 0 included basic-income-level consumption, autonomous investment, and induced consumption; for, although total autonomous investment and total induced consumption would each be greater, in any given period, in this latter case than in the case where these two components were each equal to zero in the initial period, the in1cremenzts to autonomous investment and the increments to induced consumption would, in any given period, be identical in the two cases. 2 Professor Hansen has a graphic presentation of this point: Op. Cit., p. 272. 3 This, too, is graphically presented by Hansen: ibid., p. 277. 4 Interactions Between the Multiplier Analysis and the Principle of Acceleration, this REVIEW, XXJ (I939), PP. 75-78. 5 Being concerned with governmental deficit spending, rather than with autonomous investment, Samuelson's symbol for It is gt. It is used here to give the term a more general mnemonic connotation.