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Endogenous population growth may imply chaos

Abstract

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.

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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.

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Prskawetz, A., Feichtinger, G. Endogenous population growth may imply chaos. J Popul Econ 8, 59–80 (1995). https://doi.org/10.1007/BF00172038

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  • DOI: https://doi.org/10.1007/BF00172038

Keywords

  • Population Growth
  • Periodic Solution
  • Growth Model
  • Capital Stock
  • Erratic Time