We can show, however that the conclusion about capacity shortage and surplus really applies at any time t, not only ast→>∞. For a growth rate of r implies that ()=I(0)e =r(0)e therefore, by (1)and(2), we have dt s dt s (0)e dt pl(t)=pl(ver dK The ratio between these two derivatives dr/ dt r should tell us the relative magnitudes of dx dt psWe can show, however, that the conclusion about capacity shortage and surplus really applies at any time t, not only as . For a growth rate of t →  r implies that rt I(t) = I(0)e and rt rI e dt dI = (0) therefore, by (1) and (2), we have rt I e s r dt dI dt s dY (0) 1 = = rt I t I e dt d  ( )  (0)  = = The ratio between these two derivatives, s r d dt dY dt   = should tell us the relative magnitudes of