CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 143 Substituting K=P/s into(11) we obtain Y p Since in the present case 0=8 (13) lim Yr P The expression may be called the coeficient of utilization. When the economy grows t the equilibrium rate, so that r=ao, 0=100 per cent and productive capacity is fully utilized. But as r falls below ao, a fraction of capacity a)is gradually left unused. 12 Thus the failure of the economy to grow e required rate creates unused capacity and unemployment Case 8:0<8. As investment proceeds at the rate I, new projects with a productive capacity of Is are built. Since the productive capac ity of the whole economy increases only by Io, it follows that some- where in the economy (not excluding the new projects) productive capacity is reduced by I(s-o). Therefore every year an amount of capital equal to I(s-a)/s becomes useless. The problem can now be approached from two points of view. The amounts I(s-o)/8, can be looked upon as capital losses, which are not taken into account in calculating income and investment. a In thi ase, I still indicates the rate of net investment, and all other symbols retain their old meaning, except that capital has to be redefined as the pital losse chunks of capital (over and above depreciation)are written off and junked. The annual addition to capital will then be I(8-a (15) d (16) +Io eidt= Ko+Io-(ert- 1). 1 It should be noted that if r, a, and o are constant, 0 is also a constant. Even though the to grow at the required rate, the relative disparity income does not become wider because its capital also grows not at the ut at the r rate hese losses are in the accounting sense See note 14