The theory of optimum population concerned with the stationary plateau of population considers limitations of unaugmentable land and economics of scale and maximizes per capita output and consumption. In the usual version of the growth model the slower the rate of exponential growth the higher the level of steady-state consumption. The present analysis considers differentiated periods of life work and retirement and investment in capital goods and derives the conditions for an optimum intermediate population growth rate. The analysis proves by serendipity theorem that under laisse faire private saving would suffice to support this growth-rate state if necessitated by biological and cultural factors. (AUTHORS MODIFIED)