Optimal economic growth and non-stable population

Summary This paper analyses optimal economic growth when the (exogenous) rate of population growth changes. The optimal growth path is characterized by a strikingly straightforward generalization of the traditional steady-state Golden Rule of Accumulation. The comparative statics results allow for a generalization of Samuelson's (1975) analysis of the lower-bound for the optimal rate of population growth. It is shown that under plausible assumptions the optimal savings rate follows an inverted U-shaped or U-shaped pattern during periods of demographic transition, according to whether the growth rate of births is falling or rising.