Samuelson, Population and Intergenerational Transfers

In the standard neoclassical model of Solow [12], rapid population growth is harmful to economic welfare even under the relatively benign conditions of inexhaustible resources and constant returns in production. The argument is simple: an increase in the population growth rate calls for greater investment to maintain the level of capital per head and this diverts resources from and capital deepening. The smaller the population growth rate the better. A quite different conclusion, however, follows from the familiar consumptionloan model of Samnuelson [10]. Here, in a world of overlapping generations, older people are more comfortably supported in old age by having many children. The larger the growth rate the better for per capita lifetime welfare. Recently, in a model that merges both neoclassical and consumption-loan assumptions, Samuelson [11] comes upon an intermediate position in which an increase in population growth influences welfare more positively than it would under the Solow mechanism alone.2 In fact, under plausible assumptions, the optimal growth rate may well exceed currently observed rates.3 Demographic policies are often justified by pointing to their economic implications. Samuelson's findings are therefore important and the issue deserves closer scrutiny. Let us ignore the Solow effect for the moment, and look more closely at the consumption-loan argument. Samuelson's analysis is embedded in a simple two-age model where the younger, working population supports the older, retired age group through consumption loans (transfers of that will be repaid in turn by the next generation). If a sustained increase in population growth takes place, the proportion of younger, productive people expands and the old, as a result, receive higher transfers - a bonus, in effect, from population growth. As long as the higher growth rate persists, this arrangement repeats itself every generation: everyone