Skip to main content

Capital accumulation, endogenous population growth, and Easterlin cycles

Abstract

In this paper we attempt to explain the occurrence of population cycles in industrialised economies where the birth rate depends on the difference between the actual and the expected consumption rate. This model of an endogenously growing population brings together Easterlin's idea of an adapting aspiration level with the neoclassical optimal growth paradigm. It is shown that in this highly aggregated demo-economic system (i.e., without inclusion of the age structure of a population) swings both in the economic and demographic variables may exist. The reason behind this “strange” optimal behaviour is identified to be an intertemporal substitution effect between current and future levels of consumption.

This is a preview of subscription content, access via your institution.

References

  • Ascher U, Christiansen J, Russell RD (1987) A collocation solver for mixed order systems of boundary value problems. Math Computat 33:659–679

    Google Scholar 

  • Barro RJ, Becker GS (1989) Fertility choice in a model of economic growth. Econometrica 57:481–501

    Google Scholar 

  • Becker GS, Barro RJ (1988) A reformulation of the economic theory of fertility. Qu J Econ 103:1–25

    Google Scholar 

  • Benhabib J, Nishimura K (1989) Endogeneous fluctuations in the Barro-Becker theory of fertility. In: Wenig A, Zimmermann KF (eds) Demographic change and economic development. Springer, Berlin Heidelberg New York, pp 29–41

    Google Scholar 

  • Davis EG (1969) A modified golden rule: the case of endogenous labour. Am Econ Rev 59:177–181

    Google Scholar 

  • Dockner EJ, Feichtinger G (1989) On the optimality of limit cycles in dynamic economic systems. Forschungsbericht Nr. 121 des Instituts for Ökonometrie, OR and Systemtheorie, Tech Univ Wien

  • Easterlin RA (1962) The American baby boom in historical perspective. Occasional paper no. 79, National Bureau for Economic Research, New York

    Google Scholar 

  • Easterlin RA (1968) Population, labour force and long swings in economic grwoth. National Bureau for Economic Research, New York

    Google Scholar 

  • Easterlin RA (1973) Relative economic status and the American fertility swing. In: Sheldon EB (ed) Family economic behavior: Problems and Prospects. Lippincott, Philadelphia, pp 57–74

    Google Scholar 

  • Easterlin RA (1980) Birth and fortune. The impact of numbers on personal welfare. Basic Books, New York

    Google Scholar 

  • Feichtinger G (1979) Demographische Analyse und populationsdynamische Modelle. Grundzüge der Bevölkerungsmathematik. Springer, Wien

    Google Scholar 

  • Feichtinger, G, Hartl RF (1986) Optimale Kontrolle ökonomischer Prozesse. Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften. W de Gruyter, Berlin

    Google Scholar 

  • Feichtinger G, Sorger G (1989) Self-generated fertility waves in a non-linear continuous overlapping generations model. J Popul Econ 2:267–280

    Google Scholar 

  • Feichtinger G, Sorger G (1990) Capital accumulation, aspiration adjustment, and population growth: Limit cycles in an Easterlin-type model. Math Popul Stud 2:93–103

    Google Scholar 

  • Frauenthal J, Swick K (1983) Limit cycle oscillations of the human population. Demography 20:285–298

    Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, New York

    Google Scholar 

  • Hassard BD, Kazarinoff ND, Wan YH (1981) Theory and applications of Hopf bifurcation. London Mathematical Society Lecture Notes, London

    Google Scholar 

  • Kamien MI, Schwartz NL (1981) Dynamic optimization: the calculus of variations and optimal control in economics and management. North Holland, Amsterdam

    Google Scholar 

  • Keyfitz N (1972) Population waves. In: Greville TNE (ed) Population dynamics. Academic Press, New York, pp 1–38

    Google Scholar 

  • Keyfitz N (1977) Applied mathematical demography. Wiley, New York

    Google Scholar 

  • Krelle W (1985) Theorie des wirtschaftlichen Wachstums. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Kurz M (1968) The general instability of a class of competitive growth processes. Rev Econ Stud 35:155–174

    Google Scholar 

  • Lee RD (1974) The formal dynamics of controlled populations and the echo, the boom and the bust. Demography 11:563–585

    Google Scholar 

  • Lee RD (1987a) Population regulation in humans and other animals. Presidential Address to the Population Association of America, May

  • Lee RD (1987b) Demographic forcecasting and the Easterlin hypothesis. Popul Dev Rev 2:459–468

    Google Scholar 

  • Pitchford JD (1974) Population in economic growth. North-Holland, Amsterdam

    Google Scholar 

  • Ryder HE, Heal GM (1973) Optimal growth with intertemporally dependent preferences. Rev Econ Stud 40:1–31

    Google Scholar 

  • Sato R, Davis EG (1971) Optimal savings policy when labour grows endogenously. Econometrica 39:877–895

    Google Scholar 

  • Samuelson PA (1976) An economist's non-linear model of self-generated fertility waves. Popul Stud 30:243–247

    Google Scholar 

  • Solow R (1956) A contribution to the theory of economic growth. Qu J Econ 70:65–94

    Google Scholar 

  • Steindl A (1981) Ein Kollokationsverfahren zur Lösung von Randwertproblemen bei Systemen gewöhnlicher Differentialgleichungen. Diplomarbeit, Technische Universität Wien

  • Steinmann G (1974) Bevölkerungswachstum und Wirtschaftsentwicklung. Neoklassische Wachstumsmodelle mit endogenem Bevölkerungswachstum. Duncker & Humblodt, Berlin

    Google Scholar 

  • Swick KE (1981) Stability and bifurcation in age-dependent population dynamics. Theor Popul Biol 20:80–100

    Google Scholar 

  • Tbljapurkar S (1987) Cycles in nonlinear age-structured models I. Renewal equations. Theor Popul Biol 32:26–41

    Google Scholar 

  • Wachter KW (1987) Elusive cycles: are there dynamically possible Lee-Easterlin models for U.S. birth's? Paper for presentation at the Stanford Berkeley Colloquium in Demography, November

  • Wachter KW, Lee RD (1989) U.S. births and limit cycle models. Demography 26:99–115

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We wish to thank A. Novak for helpful assistance and an anonymous referee for useful comments. Financial support by the Austrian Science Foundation under contract No. P6601 is acknowledged.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Feichtinger, G., Dockner, E.J. Capital accumulation, endogenous population growth, and Easterlin cycles. J Popul Econ 3, 73–87 (1990). https://doi.org/10.1007/BF00187285

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00187285

Keywords

  • Birth Rate
  • Population Growth
  • Demographic Variable
  • Consumption Rate
  • Optimal Growth