EVSEY D. DOMAR III. THE EFFECTS OF GROWTH Our next problem is to explore what happens when investment does grow at some constant percentage rate r, which, however, is not neces- sarily equal to the equilibrium rate ao. It will be necessary to introduce two additional concepts: average propensity to save I/y and the average ratio of productive capacity to capital P/K. To simplify the blem we shall assume that 2. P/K=8, i.e, the ratio of productive capacity to capital for the whole economy is equal to that of the new investment projects. We shall consider first the special simple more general case when 0<8.11 Case 1: 0=8. Since I=loert, capital, being the sum of all net invest- ments, equa K=Ko+Io endt=Ko+-(ert-1) As t becomes large, K will approach the expression To ert so that capital will also grow at a rate approaching r As Y=(1/a)Ioer, the ratio of income to capital is Y (10) K-10 K0+-(er-1) (11) Y T K Thus so long as r and a remain constant (or change in the same proportion) no" 'of capital takes place. This, roughly peaking, was the situation in the United States over the last seventy years or so prior to this war. 1 It is also possible that, owing to capital-saving inventions in existing plants o>s. Formally this case can be excluded by falling back on the definition of depreciation given in note 2. This, however, is not a very happy solution, but the approach used in this paper will hardly offer a better one. I think, however chat a in our society is sufficiently high to make o>s in a continuous state of full ployment more an exception than a rule