Neoclassical growth models and the optimum rate of population growth (with applications to underdeveloped countries)

Abstract

Among economists who are also interested in demography, there is a respectable tradition of analysis revolving around the concept of a static optimum population. The work of W. A. Lewis [4], J, E. Meade [5], and J. J. Spengler [12], springs to mind, for example. To these analysts, the optimum population is that which, given resources and the state of technology, maximises income per capita. It is true to say, though, that this notion of a static optimum has fallen into disfavor. The main reason is that the theory of an optimum population is, by its very nature, a dynamic question. It is concerned with the long run. And in the long run one cannot assume that resources and the state of technology are constant. A country which successfully strove to establish a static optimum population this "period" would have only a fleeting moment of achievement. Next "period," when resources (capital) have increased and technological progress has occurred, its population would be sub-optimal. The theory of a population optimum must be able to accommodate growth in resources and technological advance. One looks, therefore, for an optimum rate of growth of population (which may be negative). The appropriate analytical framework is the theory of economic growth. A second objection which may be levelled against Lewis, Meade, Spengler, etc., is their choice of maximand. Restricting oneself to purely economic maximands for the moment, income per capita is not necessarily the most appropriate. This is simple to see. Looking at the issue from an aggregate point of view--if, at maximum income per capita, all income was allocated to capital accumulation (investment) then consumption would be necessarily zero. This, one need hardly add, would probably not meet everyone's idea of a welfare maximum. Of the purely economic maximands, consumption per capita is clearly more appropriate than income per capita. (We elaborate on the non-economic components of the welfare functions later in the paper, see Section V.) We shall not be solely, even primarily, concerned with the optimum rate of growth of population for underdeveloped countries. However, when relevant and appropriate, some digressions will be made to apply the analysis in the context of their special problems.