The stable equivalent population, age composition, and Fisher’s reproductive value function

Abstract

This paper deals with a further analysis of the stable equivalent population for human populations. It first shows that the arithmetic difference between the size of the stable equivalent population and the actual population captures the total prospective contribution of age composition to the growth of the present population, if fertility and mortality rates are held constant at their current levels. The second part of the paper examines Fisher’s reproductive value function and investigates the location of maxima in relation to alternative values of the intrinsic growth rate. One conclusion which follows from this analysis is that, contrary to what has been discovered by others in specific examples, the reproductive value function can possess a global maximum in the first one or two years of life, provided the intrinsic rate of population growth is sufficiently negative. This principle is illustrated by reference to reproductive value functions calculated from the recent experience of U.S. females.