The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Optimum Population

  • J. D. Pitchford
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1671

Abstract

Malthus (1798) had argued that improvements in living standards would almost invariably call forth such an increase in population that wages would eventually be pushed back to subsistence levels. About a hundred years later Cannan (1888), Wicksell (1910) and others were writing of an optimum population, where by implication choice of family size enabled choice of living standards. A variety of measures of birth control had come into use in the 19th century, opening the prospect of permanent escape from the trap of subsistence consumption. The early optimum concept involved a population which, at some specified time, and other things such as the capital stock being held constant, resulted in maximum output per head. Clearly it is associated with the idea of first increasing and later decreasing returns in a given region with given resources and technical knowledge.

Malthus (1798) had argued that improvements in living standards would almost invariably call forth such an increase in population that wages would eventually be pushed back to subsistence levels. About a hundred years later Cannan (1888), Wicksell (1910) and others were writing of an optimum population, where by implication choice of family size enabled choice of living standards. A variety of measures of birth control had come into use in the 19th century, opening the prospect of permanent escape from the trap of subsistence consumption. The early optimum concept involved a population which, at some specified time, and other things such as the capital stock being held constant, resulted in maximum output per head. Clearly it is associated with the idea of first increasing and later decreasing returns in a given region with given resources and technical knowledge.

These discussions of what population should be gave little consideration to the fact that actual population levels are reached on the basis of private choices of family size, despite the fact that private decisions in this area had been creating a revolution in demographic experience. In the 19th century Europe went through a transition from high to low mortality because of improvements in sanitation and medical science, accompanied and followed by substantial falls in fertility due to a rising age of marriage and the adoption of various methods of birth control.

Later notions of optimum population have produced a variety of specifications of the concept. Meade (1955) argued the merits of the criterion of total utility, that is the sum of utilities of all members of the society, rather than the utility of a representative individual implied by the maximization of output or consumption per head. Often discussions of under-or over-population have been based on military, religious or cultural factors, and in the 1970s the quality of the natural environment which the population would enjoy was raised as an important issue. As well as the total utility criterion and the utility of a representative individual, the Rawlsian criterion, requiring maximization of the utility of the worst off members of society has also been used in specifying an optimum. All these criteria involve difficult philosophical issues of the rights of potential future members of the population, which are not pursued here. Production conditions assumed have ranged from constant returns to scale to the two inputs capital and labour, to variable returns to scale depending on the size of the population, capital stock and supply of fixed resources, to the assumption of depletable natural resources.

A wide version of the concept would have it include all the population levels on a path of optimal economic growth where population is chosen at any time subject to demographic constraints, and capital is accumulated according to economic constraints. The path would maximize some social welfare function over the chosen time period which might be infinite. Such problems have been analysed using optimal control techniques such as Pontryagin’s Maximum Principle and Dynamic Programming. Solving for the time paths of capital stock and various demographic variables is constrained by the fact that these techniques handle problems involving one of these variables readily, and two or more with great difficulty. Analytical insights from this literature have mainly been gained from examination of numerous versions of one, and occasionally two, dimensional models. For example, Lane (1975) treats cases in which the total utility is the maximization criterion with constant returns to capital and labour, Pitchford (1974) uses individual utility and examines the consequences of variable returns of scale, and Koopmans (1973) Cigno (1981), and Dasgupta and Mitra (1982) treat the issues raised by exhaustible resources.

The idea of an optimum population has also been associated with the theory of the provision of public goods (see, for instance, Flatters et al. 1974). The possibility of an optimum population in this context arises because an additional worker in a region will reduce the tax burden of the provision of public goods per head, but may lower the marginal product of labour. The theory of local public goods is concerned with the optimal allocation of population amongst the different communities to which these goods are specific. Another closely related issue is the idea of the optimal size of a city. Tradeoffs can occur involving increasing returns to scale in the production of factory goods at the city centre and increasing marginal costs of transport and workers’ travel time. Interesting issues are raised by the possibilities of traffic congestion and by workers’ preferences about population density in residential districts.

None of these treatments of the subject has resulted in a satisfactory method of empirically computing an optimum population path or level. Few have tried the exercise. Apart from the difficulties of finding data for estimating and solving the underlying relations, there is the problem that the future state of technical knowledge must remain an unknown factor of considerable importance. An alternative approach is to ask why the population levels and growth rates, which are the outcome of individual choices, may be considered nonoptimal. Several classes of reasons can be identified. Firstly, the observer may disagree with the criteria implicitly used in private choices of family size and may wish to see society adopt a population policy based on his own criterion. An obvious example is the desire for a large population for defence reasons, but the espousal of economic criteria such as the various social welfare functions discussed above has aspects of this approach. Secondly, various governmental policies, an example is subsidised education, may be seen to be distorting private choices with respect to family size. Thirdly, individual choices may be thought to involve externalities so not achieving a social optimum. For instance, Pazner and Razin (1980) have shown for a Samuelson consumption–loan model that, if there were perfect capital markets and perfect foresight, private choices of consumption and family size, where parents have preferences for children and have their children’s utility as an argument in their own utility functions, will lead to Pareto optimality. A variety of types of externalities may arise from individual choices. Thus individuals may have preferences about the density of population in their region, but this cannot affect economy-wide choices. Again, the output and income levels next period and so the welfare of the next generation will depend on the size of the population, yet parents may be unaware of or unable to calculate the effect of their own and society’s current fertility choices on the future size of population. Perhaps the more illuminating way to specify population policy is as a process of recognition and remedy of the possible reasons for divergence between private and social choices regarding family size. Optimal population levels and paths then become a secondary issue, being an outcome of these efforts. Nevertheless, if the concept of an optimum population is chosen in such a way as to represent the underlying population problem, the notion and the related ideas of over- and under-population could be a useful tool for elucidating, diagnosing and treating the problem.

See Also

Bibliography

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • J. D. Pitchford
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