Endogenous population growth may imply chaos

Journal of Population Economics - Tập 8 - Trang 59-80 - 1995
Alexia Prskawetz1, Gustav Feichtinger2
1Institute for Demography, Vienna, Austria
2Institute for Econometrics, Technical University, Vienna, Austria

Tóm tắt

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.

Tài liệu tham khảo

Artzrouni M, Komlos J (1985) Population growth through history and the escape from the Malthusian trap: A homeostatic simulation model. Genus 41:21–39 Artzrouni M, Komlos J (1991) A conceptualization of the industrial revolution: A search for a synthesis. Working paper Boldrin M (1988) Persistent oscillations and chaos in economic models: Notes for a survey. In: Anderson PW, Arrow KJ, Pines D (eds) The economy as an evolving complex system. Santa Fe Institute Studies in the Science of Complexity, Vol V. Addison Wesley, Redwood City, pp 49–76 Boldrin M, Woodford M (1990) Equilibrium models displaying endogenous fluctuations and chaos. J Monet Econ 25:189–222 Day RH (1982) Irregular growth cycles. Am Econ Rev 72:406–414 Day RH (1983) The emergence of chaos from classical economic growth. Q J Econ 98:201–213 Day RH, Shafer W (1992) Keynesian chaos. In: Benhabib J (ed) Cycles and chaos in economic equilibrium. Princeton University Press, Princeton NJ, pp 339–354 Day RH, Walter J (1989) Economic growth in the very long run: On the multiple-phase interaction of population, technology, and social infrastructure. In: Barnett WA, Geweke J, Shell K (eds) Economic complexity. Chaos, sunspots, bubbles and nonlinearity. Cambridge University Press, Cambridge, pp 253–289 Devaney RL (1989) An introduction to chaotic dynamical systems. Addison-Wesley, Redwood City Gumowski I, Mira C (1980) Recurrences and discrete dynamic systems (Lect Notes Math, Vol 809). Springer, Berlin Heidelberg New York Hommes CH (1991 a) Adaptive learning and roads to chaos. Econ Lett 36:127–132 Hommes CH (1991 b) Chaotic dynamics in economic models. Some simple case-studies. Groningen Theses in Economics, Wolters-Noordhoff, Groningen Kennedy P (1992) Preparing for the Twenty-First Century. Random House, New York Lee RD (1986) Malthus and Boserup: a dynamic synthesis. In: Coleman D, Schofield R (eds) The state of population theory: Forward from Malthus. Basil Blackwell, New York, pp 96–130 Li TY, Yorke A (1975) Period three implies chaos. Am Math Mon 82:985–992 Lorenz HW (1993) Nonlinear dynamical economics and chaotic motion. Springer, Berlin Heidelberg New York Lorenz HW (1992) Multiple attractors, complex basin boundaries, and transient motion in determnistic economic systems. In: Feichtinger G (ed) Dynamic economic models and optimal control. North-Holland, Amsterdam Malthus TR (1798) An essay on the principle of population as it affects the future improvement of society. London van Marrewijk C, Verbeek J (1993) On opulence driven poverty traps. J Popul Econ 6:67–81 Medio A (1992) Chaotic dynamics. Theory and application to economics. Cambridge University Press, Cambridge Prskawetz A (1992) Nichtlineare Demoökonomie. Thesis at the Technical University of Vienna Prskawetz A, Feichtinger G, Wirl F (1994) Endogenous population growth and the exploitation of renewable resources. Math Popul Stud 5(1):87–106 Sanderson CW (1980) Economic-demographic simulation models: a review of their usefulness for policy analysis. HASA Report, RR-80-14, Laxenburg, Austria Solow RM (1956) Contribution to the theory of economic growth. Q J Econ 70:65–94 Steinmann G (1984) A model of the history of demographic-economic growth. In: Steinmann G (ed) Studies in contemporary economics. Economic consequences of population change in industrial countries. Springer, Berlin Heidelberg New York, pp 29–49 Tunzelmann GN (1986) Malthus's ‘total population system’: a dynamic reinterpretation. In: Coleman D, Schofield R (eds) The state of population theory. Forward from Malthus. Basil Blackwell, New York, pp 65–95 Tunzelmann GN (1991) Malthus's evolutionary model, expectations, and innovation. J Evolut Econ 1:273–291 Turner M (1986) Malthus and his time. Macmillan Press, Basingstoke Wiggins S (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, New York Winegarden CR, Wheeler M (1992) The role of economic growth in the fertility transition in Western Europe: econometric evidence. Economica 59:421–435