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Frontmatter

Optimum Population: An Introduction

Optimum Population: An Introduction

Abstract
The Malthusian threat of overpoulation has inspired many writers ever since Thomas Robert Malthus’ “Essay on the Principle of Population” appeared in 1798 (and 1830). Because the Malthusian framework is basically economic, the population question has always attracted many economists. Malthus hypothesised that families procreate to the point where they are living at the level of subsistence. “Before that a large and increasing population was generally favored; since that date it has never creased to be looked upon by some doubt and with fear.… Before Malthus the criterion was the prosperity of the sovereign and of the ruling classes; thereafter it became the welfare of the increasing masses.” (Fetter, 1913, p. 4)
Klaus F. Zimmermann

Optimal Size and Growth Rate of Population

Frontmatter

Socially Optimal Population Size and Individual Choice

Abstract
Since Becker’s (1960) analysis, the implications of endogenous fertility in the sense of parental altrusim towards their own children, for consumption, labor supply and household unemployment decisions have been explored extensively in the literature. The purpose of this paper is to examine the general equilibrium implications of endogenous fertility for a number of social issues of population policy. We are thus concerned with the normative rather than the positive implications of endogenous fertility. In our analysis, we adopt the simplest possible formulation: In addition to their own consumption, the number of children and the utility of each child is assumed to enter the utility function of the parents. Thus, subject to whatever economic opportunities and constraints they face, parents are assumed to maximize their own utility functions (one per couple) in making choices with respect to numbers of children and investments in them. Noncoersive tax and subsidy policies may be devised to affect these decisions; in the absence of such policies, a laissez-faire solution will generally exist. We ask first whether the laissez-faire solution will be efficient from the standpoint of the present generation, that is, whether individual choice in the absence of social intervention will lead to a Pareto-optimal solution. We next introduce the notion of an intergenerational social welfare function and ask whether laissez-faire leads to a social optimum under various criteria and, if not, what non-coercive social policies may be introduced to achieve one.
Marc Nerlove, Assaf Razin, Efraim Sadka

Endogenous Population With Discrete Family Size and a Capital Market

Abstract
The work of Becker (1960, 1981) on the economics of the family where the number and the “quality” of children are endogenous has in recent years given rise to studies in population policy such as Nerlove et al. (1984) and Kemp et al. (1983). In these analyses the number of children a family chooses to have and the size of the bequest left to them are the result of utility maximization by a typical family; hence the size and age structure of the population can be made endogenous and the effect on them of various policy parameters can be studied.
Daniel Leonard

Is There an Optimal Growth Rate for Population?

Abstract
This contribution discusses the existence and properties of population growth rates which are optimal in the sense of (1) the number of children and retirees which the average active person has to support, i.e. the overall demographic dependency rate is minimized, (2) the economic dependency rate, i.e. the relative share of per-capita income which the average active person has to spend in order to support children and retirees is minimized and (3) net per-capita consumption, i.e. per-capita income less dependency burden of the average active person is maximized. The corresponding optimal population growth rates are denoted by n*, n**, and n*** respectively.
Gerhard Schmitt-Rink

Technical Progress and Social Security

Frontmatter

Technological Change and Population Growth

Abstract
In the Malthusian and Ricardian tradition, economic development is viewed as a race between population and technical improvements. Technological change is envisaged as an outward shift of the production possibility frontier which opens new space to be filled with a growing population. Upon technical improvements, population size increases until the enlarged consumption possibilities are exhausted and consumption per head has come down to a stationary subsistence level again. Hence, according to this view, technical improvements elicit accelerated population growth. It will be shown in this paper that, from a neoclassical point of view, technical progress under quite reasonable assumptions lowers population growth.
Manfred Neumann

The Serendipity Theorem Reconsidered: The Three-Generations Case Without Inheritance

Abstract
In his article on the optimum growth rate for population Samuelson (1975) proved within a two-generations model (individuals live and consume for two periods, but provide labor in the first period only) his famous so-called Serendipity Theorem: “At the optimum growth rate g*, private lifetime saving will just support the most golden golden-rule lifetime state”. The underlying theory of optimum growth rate for population was criticized mainly on two partly-related grounds: (i) Deardorff (1976) pointed out that Samuelson’s solution for the optimum population growth rate g*, derived only from necessary conditions for optimality, is in fact not optimal in general. In the special case in which both utility and production functions are Cobb-Douglas, Samuelson’s solution, for those parameter values for which it exists, provides a global minimum of steady-state utility. Moreover, Deardorff proved that for CES production functions with substitution elasticity (σ) greater than unity, steady-state utility can be made arbitrarily large by taking g sufficiently close to -δ (the depreciation rate). In his reply to Deardorffs note, Samuelson (1976) agreed with Deardorffs analysis and results. In addition he mentioned an argument first brought up by Mirrlees: If σ remains bounded above zero as the capital intensity k approaches infinity, for most reasonable forms of the utility function, the solution g* = must be a local boundary maximum with finite utility.
Klaus Jaeger

Limited Resources

Frontmatter

Endogenous Population and Fixed Input in a Growth Model With Altruism

Abstract
Analyses of economic growth may treat population as an independent variable or as an endogenous one. To each of these two approaches may be associated a certain theoretical view of growth. Modern growth theories in the tradition of Ramsey and Solow are based on a constant proportional rate of population growth as the essential driving force of the mechanism with perhaps some aid from technological progress. The classical economists, especially Ricardo, rely on the idea that in the presence of fixed inputs per capita consumption tends eventually to fall and to reach a floor at which population stops growing. Dividing these two views, there is not only the question of whether population is independent of economic considerations but also that of whether there is a natural resource constraint that cannot be removed by substitution with reproductible inputs or by technological progress.
Pierre Pestieau

On the Malthusian Hypothesis and the Dynamics of Population and Income in an Equilibrium Growth Model With Endogenous Fertility

Abstract
In this paper we analyze two positive issues regarding population and economic growth. The first issue concerns the pessimistic conjecture of Malthus that the existence of a fixed amount of land leads to the eventual decline in per-capita consumption and capital.1) The second issue concerns the observed positive association between population growth and income growth in developed countries (Kuznetz (1966)). To analyze these issues we use a version of the overlapping generations growth framework in which fertility is subject to individual choice.2)
Zvi Eckstein, Steve Stern, Kenneth I. Wolpin

Choice of Fertility and Population Pressure in Traditional Rural Societies

Abstract
Since Malthus’s “Essay on Population” (1798) classical economics regarded the theory of population as an integral part of political economy. Neoclassical economics maintained the interest in the question of population but, under the influence of utilitarianism, gave it a somewhat different direction. Level and growth of population took on more and more the character of exogenous variables which influence the outcome of the economic process but are no longer explained by means of the same analytical apparatus that was employed to understand the behavior of the endogenous economic variables. If the level or growth of population was considered the subject of rational choice, it was in the context of normative analysis where the choices are made by a fictitious benevolent dictator but not by the people themselves (see, e. g., Lane, 1977). In the non-normative long-run equilibrium models of neoclassical growth theory population was just assumed, with some remarkable exceptions (e. g., Meade, 1968), to grow at a constant exogenously given rate. Moreover, growth theorists did not, as demographers have been used to, pay attention to the different age cohorts of which the total population is made up. Mainly two developments in economic theory changed the picture completely: One was the explicit introduction of age cohorts or overlapping generations into models of long-run economic equilibrium by Samuelson (1958) which, though still treating population growth as an exogenous variable, revolutionized the analysis of intertemporal equilibria of economies with an infinite time horizon made up of finitely lived individual agents.
Gerhard Schwödiauer, Alois Wenig

International Economics

Frontmatter

Economic Interdependence and Optimum Population: An Examination of Meade’s Objection to the Individual Utility Criterion

Abstract
Meade (1955) devoted a chapter of his Trade and Welfare volume to optimum population and optimum saving. In this discussion he finds reasons for abandoning individual welfare as a criterion for optimum population in favour of the use of total utility. His objection to individual, or as he calls it “per caput” utility is worth quoting in full.
John D. Pitchford

An Analysis of International Migration: The Unilateral Case

Abstract
Any fully satisfactory analysis of population change, whether of the descriptive variety or of the welfare-theoretical variety, must contain within it a satisfactory analysis of the international migration of labour. However in the analysis of migration pitfalls abound; as a result, the subject remains in a quite primitive state, for the most part simply aping the theory of long-term international capital flows. In particular, the analysis of migration lacks a firm basis in the decision-making of individual households. Exempted from these comments is the recent paper by Galor (1986). That paper will be discussed at the end of Section 2.
Murray C. Kemp, Hitoshi Kondo

Population, International Trade and Indebtedness: A More General Analysis

Abstract
Our purpose in the present paper is to develop an open-economy, overlapping-generations model in which population, international trade and international indebtedness all appear as endogenous variables and in which intergenerational caring and bequests play a role. In particular, we examine the effects of international trade and investment on the steady-state values of capital ownership per worker, the capital-labour ratio, the level of income per family and the rate of population growth.
Hitoshi Kondo

Backmatter

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