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Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice

Author

Listed:
  • Takao Asano

    (Okayama University)

  • Akihisa Shibata

    (Kyoto University)

  • Masanori Yokoo

    (Okayama University)

Abstract

This paper constructs a simple overlapping generations (OLG) model with the working and capitalist classes and two types of production technologies. The behavior of agents belonging to the working class is basically the same as that in the standard Diamond (1965) type OLG model, whereas agents belonging to the capitalist class face two available technologies, select the one with a higher return on capital, and bequeath their assets to the next generation without supplying labor. Using techniques concerning the circle map in dynamical systems theory, we show that in an extreme case in which one technology is linear and the other is of the Leontief type, the economy exhibits bounded, non-periodic but non-chaotic motions for a large set of parameter values. We provide explicit formulas for the rotation number and the absolutely continuous invariant probability measure of our model.

Suggested Citation

  • Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice," KIER Working Papers 1070, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:1070
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    References listed on IDEAS

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    1. Azariadis, Costas & Reichlin, Pietro, 1996. "Increasing returns and crowding out," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 847-877, May.
    2. Asano Takao & Yokoo Masanori & Shibata Akihisa, 2023. "Middle-income traps and complexity in economic development," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(4), pages 553-565, September.
    3. Eberhardt, Markus & Presbitero, Andrea F., 2015. "Public debt and growth: Heterogeneity and non-linearity," Journal of International Economics, Elsevier, vol. 97(1), pages 45-58.
    4. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    5. Kiminori Matsuyama, 2007. "Credit Traps and Credit Cycles," American Economic Review, American Economic Association, vol. 97(1), pages 503-516, March.
    6. Farmer, Roger E. A., 1986. "Deficits and cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 77-88, October.
    7. Gabriel Zucman, 2019. "Global Wealth Inequality," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 109-138, August.
    8. Yokoo, Masanori, 2000. "Chaotic dynamics in a two-dimensional overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 909-934, June.
    9. Liuchun Deng & Minako Fujio & M. Ali Khan, 2021. "Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 615-639, September.
    10. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
    11. Ishida, Junichiro & Yokoo, Masanori, 2004. "Threshold nonlinearities and asymmetric endogenous business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 175-189, June.
    12. Pintus, Patrick & Sands, Duncan & de Vilder, Robin, 2000. "On the transition from local regular to global irregular fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 247-272, February.
    13. Azariadis, Costas & Smith, Bruce, 1998. "Financial Intermediation and Regime Switching in Business Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 516-536, June.
    14. Mattauch, Linus & Klenert, David & Stiglitz, Joseph E. & Edenhofer, Ottmar, 2022. "Overcoming wealth inequality by capital taxes that finance public investment," Structural Change and Economic Dynamics, Elsevier, vol. 63(C), pages 383-395.
    15. Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    16. Umezuki, Yosuke & Yokoo, Masanori, 2019. "A simple model of growth cycles with technology choice," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 164-175.
    17. Takuma Kunieda & Akihisa Shibata, 2014. "Credit Market Imperfections and Macroeconomic Instability," Pacific Economic Review, Wiley Blackwell, vol. 19(5), pages 592-611, December.
    18. Iwaisako, Tatsuro, 2002. "Technology choice and patterns of growth in an overlapping generations model," Journal of Macroeconomics, Elsevier, vol. 24(2), pages 211-231, June.
    19. Kunieda, Takuma & Shibata, Akihisa, 2017. "Entrepreneurs, Financiers, And Boom–Bust Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 21(3), pages 785-816, April.
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    Cited by:

    1. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2024. "Technology choice, externalities in production, and a chaotic middle-income trap," Journal of Economics, Springer, vol. 141(1), pages 29-56, January.

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    More about this item

    Keywords

    Endogenous business cycles; technology choice; quasi-periodic motion; OLG model; rotation numbe;
    All these keywords.

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