Endogenous population growth may imply chaos

We consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, we obtain numerical results on the qualitative behaviour of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies — assumed to be characterised by low and high savings rate respectively — are characterised by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.This work was supported by a grant from the Austrian Academy of Sciences. G. Feichtinger acknowledges financial support from the Austrian Science Foundation under contract No. P 9608-SOZ. The helpful comments of C. H. Hommes, G. Lee and of an anonymous referee are gratefully acknowledged.     

Renewable resources and population growth: Past experiences and future prospects

The links between population growth, resource use, and environmental quality are too complex to permit straightforward generalizations about direct causal relationships. Rapid population growth, however, has increased the number of poor people in developing countries, thus contributing to the degradation of the environment and the renewable resources of land, water, and nonhuman species on which humans depend. Demands of the rich industrial countries have also generated environmental pressures and have been foremost in the consumption of the so-called nonrenewable resources: fossil fuels, metals, and minerals. On the other hand, population and economic growth have also stimulated technological and management changes that help supply and use resources more effectively. Wide variations in the possible ultimate size of world population and technological change make future interrelationships of population, resources, and the environment uncertain as well as complex. But those interrelationships are mediated largely by government policies. Responsible governments can bring about a sustainable balance in the population/resource/environment equation by adopting population and development policies that experience has shown could reduce future population numbers in developing countries below the additional five billion indicated in current United Nations medium projections, coupled with proven management programs in both developing and developed countries that could brake and reverse the depletion and degradation of natural resources.This article is adapted from: Robert Repetto, "Population, Resources, Environment; An Uncertain Future,"Population Bulletin, Vol. 42, No. 2 (Washington, D.C.: Population Reference Bureau, 1987).     

Endogenous fertility,mortality and growth

Economic and demographic outcomes are determined jointly in a choice-theoretic model of fertility, mortality and capital accumulation. There is an endogenous population of reproductive agents who belong to dynastic families of overlapping generations connected through altruism. In addition to choosing savings and births, parents may reduce (infant) deaths by incurring expenditures on health-care which is also provided by the government. A generalised production technology accounts for long-run endogenous growth with short-run transitional dynamics. The analysis yields testable time series and cross-section implications which accord with the empirical evidence on the relationship between demography and development. Received: 22 April 1996 / Accepted: 2 April 1998     

World food resources and population: the narrowing margin

This bulletin examines the narrowing margin between global food production and population growth. Between 1950 and 1971, world grain production nearly doubled and per capita production increased 31%. During the 1970s, gains in output barely kept pace with population growth, consumption/person declined in sub-Saharan Africa and parts of Asia, food prices were volatile, and over 100 food deficit countries came to depend on the exportable surplus of North America, now the only major grain exporting region. The world fish catch levelled off in the early 1970s and beef production, still dependent mainly on grassland grazing, levelled off in the mid-1970s. With little new land left to plow, satisfying increased food demand now depends on sharp increases in yields on existing crop land. Worldwide, this effort is hampered by loss of topsoil and irrigated land, conversion of cropland to nonfarm uses, rising energy costs, inefficient agrarian structures, particularly in the Soviet Union, the falling yield response to chemical fertilizers in agriculturally advanced countries, and the emerging competition between food and agriculturally based energy crops. Green Revolution successes in some developing countries deomonstrate that, given the right inputs, 3rd world farmers can increase crop yields dramatically. Feeding the world's poor also requires more equitable income and food distribution, including a reduction in the proportion of grain and fish consumed indirectly as livestock products by the affluent. Most important in meeting food needs on a finite planet is braking population growth. The author concludes that every effort should be made to stabilize world production at abour 6 billion by 2020, rather than 10.5 billion by 2110, as is now projected by the UN.     

Polygyny and the rate of population growth

Summary The roots, motives and feasibility of practising polygyny in societies with a balanced sex structure and the effect of polygyny on the rate of population growth are considered. High demand for labour combined with limited supply over the last several centuries, had been conducive to the evolution of a polygynous nuptiality pattern. The unprecedentedly high rates of population growth during the last several decades combined with progressive economic development have led to a change in the role of the labour factor and consequently diminished its impact upon polygyny. Polygyny is feasible because of a sex-age differential at first marriage, which enables younger cohorts of women to enter the marriage market, and thus results in a very early age at first marriage and universal incidence of marriage among women. A very young pattern of nuptiality inevitably evolves under polygyny, which tends to raise the rate of population growth. No significant variation in fertility between polygynous and monogamous women was found but substantial gaps in standards of living, child mortality, and educational attainment were noted for polygynous households. The findings imply that during the transition from polygyny to monogamy family size will tend to diminish, although initially fertility may not decline concurrently with changing socio-economic status. The most important effects on the rate of population growth thus result from the increase in age at first marriage and declining proportions of ever married women.     

学龄人口变动与人力资源——基于重庆市2005-2020年学龄人口变动的探讨

教育投资的对象是人,而人口作为个体人的集合,其变动必然对教育产生各种各样的影响。本文以重庆为例,在对重庆市人力资源开发现状、2005-2020年学龄人口发展状况和现存教育资源充分分析的基础上,对重庆市未来教育资源整合、提升人力资源开发层次等问题进行探讨并提出一点政策建议。     

Nuptiality and population growth

In the European historical experience, nuptiality patterns played a very significant role in the development of low fertility. Late marriage and widespread celibacy provided one of the mechanisms by which age-specific fertility rates were brought to low levels in the populations of Western Europe. In Eastern and Central Europe on the other hand, where marriage customarily occurred earlier and was more nearly universal, a somewhat slower fertility transition was achieved through a reduction in marital fertility — without any drastic accompanying nuptiality change. Populations of developing countries, however, commonly exhibit nuptiality patterns characterized by a still higher incidence and a considerably younger age-pattern of marriage than even the earliest observed schedule from Eastern Europe. With few exceptions, little work has been done to date to examine the implications of these very early and universal marriage schedules for fertility in general and for the growth of these populations in particular.¹ We have therefore tried to analyse the impact of nuptiality on the fertility and growth of a series of populations from developing nations where extra-marital fertility is negligible. Populations in which the prevalence of cohabitation by age is not well documented by existing marital-status data (mainly those in Latin America and tropical Africa) are excluded from this analysis; an attempt will be made in later work, however, to extend the analysis to these populations.     

Nuptiality and population growth

Abstract In the European historical experience, nuptiality patterns played a very significant role in the development of low fertility. Late marriage and widespread celibacy provided one of the mechanisms by which age-specific fertility rates were brought to low levels in the populations of Western Europe. In Eastern and Central Europe on the other hand, where marriage customarily occurred earlier and was more nearly universal, a somewhat slower fertility transition was achieved through a reduction in marital fertility - without any drastic accompanying nuptiality change. Populations of developing countries, however, commonly exhibit nuptiality patterns characterized by a still higher incidence and a considerably younger age-pattern of marriage than even the earliest observed schedule from Eastern Europe. With few exceptions, little work has been done to date to examine the implications of these very early and universal marriage schedules for fertility in general and for the growth of these populations in particular.(1) We have therefore tried to analyse the impact of nuptiality on the fertility and growth of a series of populations from developing nations where extra-marital fertility is negligible. Populations in which the prevalence of cohabitation by age is not well documented by existing marital-status data (mainly those in Latin America and tropical Africa) are excluded from this analysis; an attempt will be made in later work, however, to extend the analysis to these populations.     

Relating briefly the natural resources and the population problems of China]

Problems in population, manifested primarily as either "over" or "under" population, are ultimately related to the development of natural resources. Land is the most basic of natural resources. China's land mass is largely mountainous, with 56% of its more than 2000 counties, 1/3 of its population, 40% of its cultivated land and a majority of its forests, situated in mountainous regions. The quality and the distribution of the various kinds of land are complex and uneven. Although China is rich in forests, grazing, and arable land compared to the rest of the world, its 1 billion population makes the land a limited resource. The limitations of the land are also seen in soil erosion, soil that is increasingly turning into sand, and deforestation. Water resources are not considered scarce, yet compared to the rest of the world, it is limited. Its distribution is very uneven, with more water in the east and west, and less in the north and south. In the southwest mountainous border regions, for instance, water is abundant, but the population and arable land there is such that the demand for water is low. Moreover, droughts and heavy precipitation make the annual water supply unpredicatable. The demand for water becomes increasingly greater as agricultural production develops further, the population increases and as the cities continue to expand. living matter as a resource includes all the animal and plant life that is necessary for livelihood, but only forests and grasslands are discussed here. China's forests, if their use is not abused, can serve as a continuous supply for manufactured products. But its distribution is uneven and sparse. Population control will be ineffective if the forests are not replenished and developed. Grasslands are the primary source for animal products. The natural grasslands, found mainly in the north and west, are not as productive as that of other nations due to the nature of China's topography, the vagaries of climate, and deterioration. Energy, the source for fuel, includes such natural resources as coal, petroleum, natural gas, hydraulic, and solar power. China is among the world's richest in energy resources, yet the supply is sometimes insufficient when spread among 1 billion people.     

On the momentum of population growth

If age-specific birth rates drop immediately to the level of bare replacement the ultimate stationary number of a population will be given by (9): $$\left( {{\textstyle{{b\mathop e\limits^ \bullet {}_0} \over {r\mu }}}} \right)\left( {\frac{{R_0 - 1}}{{R_0 }}} \right)$$ multiplied by the present number, where b is the birth rate, r the rate of increase, \(\mathop e\limits^ \bullet _0 \) the expectation of life, and R ₀ the Net Reproduction Rate, all before the drop in fertility, and μ the mean age of childbearing afterwards. This expression is derived in the first place for females on the stable assumption; extension to both sexes is provided, and comparison with real populations shows the numerical error to be small where fertility has not yet started to drop. The result (9) tells how the lower limit of the ultimate population depends on parameters of the existing population, and for values typical of underdeveloped countries works out to about 1. 6. If a delay of 15 years occurs before the drop of the birth rate to replacement the population will multiply by over 2. 5 before attaining stationarity. The ultimate population actually reached will be higher insofar as death rates continue to improve. If stability cannot be assumed the ultimate stationary population is provided by the more general expression (7), which is still easier to calculate than a detailed projection.     

Urban growth and population densities

Differences in the distribution of population within and across metropolitan areas are seen as a product of the development of the metropolis during different transportation epochs. Age cohorts of census tracts in Cleveland, Ohio, may be split into three groups of development patterns based on the time of their early development: (1) before the development of the automobile, (2) during the early period of the auto’s diffusion to the population, and (3) during the period of the mass diffusion of the auto. Patterns of population concentration and congestion across metropolitan areas are heavily selective of places with large population growth before the development of the streetcar and the automobile. More recent population growth has had little effect on population congestion but has led to a deconcentrated metropolis.     

Utilitarian tradeoff between population growth and income growth

Utilitarian social welfare functions were devised for a world with a fixed population. With endogenous population, Edgeworth conjectured that the Benthamite principle of maximizing total utility (classical utilitarianism) would lead to a larger population size and a lower standard of living than the Millian principle of maximizing per capita utility (average utilitarianism). One objection to the Benthamite criterion was that its application to a world with finite resources often implied large population size in conjunction with an embarrassingly low average standard of living. In a static environment with altruistic parents, this may not be warranted. In a growth situation, this criticism is even less likely to be supported. This paper extends the comparison of classical and average utilitarianism from a static to a dynamic and endogenously growing economy. Using a stylised endogenous growth framework, it confirms that the Benthamite population growth rate exceeds the Millian growth rate. In terms of the rate of growth of per capita income, the reverse is true. Having the standard of living often increasing under the Benthamite criterion, our results thereby depart significantly from the repugnant conclusion levelled against classical utilitarianism.We would like to thank an anonymous referee for helpful suggestions.     

World population growth and the food supply]

The general trend in the last several hundred years has been that the speed of growth in the food supply exceeds the speed of the population growth. For the time being, 2 major problems still exist. The 1st problem is that food production is still influenced by natural conditions. For example, abnormal weather conditions may cause regional food shortages. The 2nd problem is the imbalance of food consumption by the world population. This phenomenon exists between different social classes as well as between developed and developing countries. According to statistics released by the World Bank, 1 billion suffer from malnutrition today and most of them are in developing countries. In developed countries, about half of their increase in the food supply is for feed grains, and those countries follow the policy of reducing farm land for the purpose of maintaing stabl e grain prices. Up to the present time, grain prices have been unstable, and this has become a rather heavy economic burden for numerous developing countries. Many developing countries are trying to increase grain production by increasing their arable land and promoting their cultivating techniques. However, these countries are facing the problems of finding and adequate water supply, fertilizer, and pesticides. In addition, a rapid population growth in these countries has offset their endeavors in agriculture. In recent years, these counties have realized the necessity of birth control. The world population growth rate has decreased from 2% to about 1.7% in 1981. Birth control and an increase in the food supply will bring new hope to the world's problems of overpopulation and food supply.     

Endogenous fertility and human capital in a Schumpeterian growth model

This study develops a scale-invariant Schumpeterian growth model with endogenous fertility and human capital accumulation. The model features two engines of long-run economic growth: R&D-based innovation and human capital accumulation. One novelty of this study is endogenous fertility, which negatively affects the growth rate of human capital. Given this growth-theoretic framework, we characterize the dynamics of the model and derive comparative statics of the equilibrium growth rates with respect to structural parameters. As for policy implications, we analyze how patent policy affects economic growth through technological progress, human capital accumulation, and endogenous fertility. In summary, we find that strengthening patent protection has (a) a positive effect on technological progress, (b) a negative effect on human capital accumulation through a higher rate of fertility, and (c) an ambiguous overall effect on economic growth.     

Developing population science and making it serve the goal of controlling population growth]

This is the text of a speech delivered at the Third National Population Science Discussion Meeting, held on February 27, 1981. The author summarizes past achievements of the Chinese program to control the rate of population growth, emphasizes the importance of the program's success for the well-being of future generations, and discusses the research needed to make it successful. Attention is given to how Chinese attitudes toward the family need to be changed to encourage the one-child family.     

Endogenous fertility,endogenous lifetime and economic growth: the role of child policies

We examine the effects of child policies on both transitional dynamics and long-term demo-economic outcomes in an overlapping-generations neoclassical growth model à la Chakraborty (J Econ Theory 116(1):119–137, 2004) extended with endogenous fertility under the assumption of weak altruism towards children. The government invests in public health, and an individual’s survival probability at the end of youth depends on health expenditure. We show that multiple development regimes can exist. However, poverty or prosperity does not necessarily depend on the initial conditions, since they are the result of how a child policy is designed. A child tax, for example, can be used effectively to enable those economies that were entrapped in poverty to prosper. There is also a long-term welfare-maximising level of the child tax. We show that a child tax can be used to increase capital accumulation, escape from poverty and maximise long-term welfare also when (a) a public pay-as-you-go pension system is in place and (b) the government issues an amount of public debt. Interestingly, there also exists a couple child tax–health tax that can be used to find the second-best optimum optimorum. In addition, we show that results are robust to the inclusion of decisions regarding the child quantity–quality trade-off under the assumption of impure altruism. In particular, there exists a threshold value of the child tax below (resp. above) which child quality spending is unaffordable (resp. affordable) and different scenarios are in existence.     

Canada's population: growth and dualism

In Canada the current 1.3% population growth rate is causing some concern. Those concerned argue that such a rate of growth in combination with high levels of consumption could jeopardize the country's resource base and its comfortable style of living. Many Canadians are questioning high levels of immigration, for now that the fertility level is below replacement level, net immigration contributes substantially to population growth (over 1/3 in 1976). The growing proportion of non-Europeans among recent immigrants is causing resentment, and, in a tight job market, immigrants are regarded as threats to the World War 2 baby boom cohort who are now at working ages. The baby boom generation also puts stress on housing and health services, and it will increase the need for pension checks as it ages. Although French fertility is no longer high and immigration is no longer dominated by the British, the French group's 200-year struggle to preserve its identity continues on in the current effort of the Quebec government to enforce the use of French language by law within that province. Geography and climate dictate another demographic fact that divides the country and pervades its history. In addition to intense regionalism, uneven population distribution is responsible for 2 other concerns: the rapid growth of several already large cities and depopulation of many small communities. Focus in this discussion is on Canada's population growth in the past and as projected for the future, historical and current fertility, mortality and immigration trends, the search for a new immigration policy, the impact of the baby boom generation on the population's age structure and the problems this creates, and recent shifts in population distribution and in the country's ethnic and linguistic makeup. The population policy proposals evolved thus far involve to a great extent the use of immigration as a lever for achieving given population objectives.     

Optimal age of retirement and population growth

The purpose of this paper is to study intergenerational optimal resources sharing when the social planer can choose the retirement age in addition to consumptions and investment. We use the extension of the Diamond analysis by Hu [1979] that incorporates endogenous retirement age. We found that the optimal retirement age is an increasing function of the population growth rate if the elasticity of substitution of old agents' labor for young agents' labor is lower than one. In the millian case, when the size of a population does not matter, and when the elasticity of substitution of old agents' labor for young agents' labor is strictly higher than one, the optimal retirement age is a decreasing function of the population growth rate. In the benthamite case, the change in the optimal retirement age is indeterminate. Received: 19 February 1999/Accepted: 27 February 2001 All correspondence to Bertrand Crettez. We would like to thank Jean-Pierre Vidal for very helpful comments on an earlier draft. An anonymous referee provided insightful comments on a previous version of this paper. Responsible editor: Alessandro Cigno.