CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 141 Let the economy be in an equilibrium position so thatio To retain the equilibrium position, we must have dp dy dt dt Substituting(2)and (3)into(5) we obtain our fundamental equation the solution of which gives ao is the equilibrium rate of growth. So long as it remains constant the maintenance of full employment requires investment to grow at a con- If, as a crude estimate, a is taken at 12 per cent and o at some 30 per cent, the equilibrium rate of growth will be some 3. 6 per cent per The reader will now see that the assumption of constant a and o is not entirely necessary, and that the whole problem can be worked out with variable a and g formation to national income)was fairly constant and approximately equal to some 12 per cent. See Simon Kuznets, National Product Since 1869, National Bureau of Economic Research (mimeographed, 1945)p. II-89 and the Survey of Current Business, Vol. 22, May, 1942, and Vol. 24, April, 1944. In a problem of rclical character, an assumption of a constant propensity to save would be very bad. Since we are interested here in a secular problem of continuous full employ ment, this assumption is not too dangerous 10 The problem can be also worked out for the case when Po>Yo. oa After this paper was sent to the printer I found a very interesting article by E. H Stern, "Capital Requirements in Progressive Economies, "Economica, Vol. 12, August, 1945, pp. 163-171, in which the relation between capital and utput in the U. S. during 1879-1929 is expressed (in billions of dollars )as capital 3.55. My estimates gave roughly similar results. This would place s around 30 per cent, though this figure should be raised to account for the underutilization of capital during a part of that period. It is also not clear how che junking process(see p. 144)was reflected in these figures. Review, Vol 34, December, 1944