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Business Cycles in a Two-Sided Altruism Model

Author

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  • Hiroshi Fujiu

    (Department of Economics, Chiba Keizai University, 3-59-5 Todoroki, Inage, Chiba 263-0021, Japan)

Abstract

This study demonstrates that business cycles with complex periodic fluctuations may arise in an overlapping generations model with two-sided altruism. The structure of an equilibrium dynamical system strongly depends on the degree of altruism in the model. If either altruism of a generation to the parent or the child disappears, the study also demonstrates that complex periodic fluctuations never occur. In this sense, two-sided altruism is essential for a complex business cycle.

Suggested Citation

  • Hiroshi Fujiu, 2021. "Business Cycles in a Two-Sided Altruism Model," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2054-:d:622229
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    References listed on IDEAS

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    1. Hori, Hajime, 1992. "Utility functionals with nonpaternalistic intergenerational altruism: The case where altruism extends to many generations," Journal of Economic Theory, Elsevier, vol. 56(2), pages 451-467, April.
    2. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2016. "Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 299-309.
    3. Kazuo Nishimura & Makoto Yano, 2012. "On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 165-191, Springer.
    4. Gonzalez, Francisco M. & Lazkano, Itziar & Smulders, Sjak A., 2018. "Intergenerational altruism with future bias," Journal of Economic Theory, Elsevier, vol. 178(C), pages 436-454.
    5. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    6. Deng, Liuchun & Khan, M. Ali, 2018. "On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 46-55.
    7. Lane, John & Mitra, Tapan, 1981. "On Nash Equilibrium Programs of Capital Accumulation under Altruistic Preferences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 309-331, June.
    8. Hori, Hajime, 1997. "Dynamic Allocation in an Altruistic Overlapping Generations Economy," Journal of Economic Theory, Elsevier, vol. 73(2), pages 292-315, April.
    9. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    10. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2019. "Dynamics of a generalized fashion cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 135-147.
    11. Simone Marsiglio & Marco Tolotti, 2018. "Endogenous growth and technological progress with innovation driven by social interactions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 293-328, March.
    12. Takaaki Aoki & Kazuo Nishimura, 2017. "Global convergence in an overlapping generations model with two-sided altruism," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1205-1220, November.
    13. Kohlberg, Elon, 1976. "A model of economic growth with altruism between generations," Journal of Economic Theory, Elsevier, vol. 13(1), pages 1-13, August.
    14. B. Douglas Bernheim & Debraj Ray, 1987. "Economic Growth with Intergenerational Altruism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 227-243.
    15. Nishimura, Kazuo & Yano, Makoto, 1994. "Optimal Chaos, Nonlinearity and Feasibility Conditions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 689-704, August.
    16. Fujio, Minako, 2008. "Undiscounted optimal growth in a Leontief two-sector model with circulating capital: The case of a capital-intensive consumption good," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 420-436, May.
    17. Hori, Hajime & Kanaya, Sadao, 1989. "Utility functionals with nonpaternalistic intergenerational altruism," Journal of Economic Theory, Elsevier, vol. 49(2), pages 241-265, December.
    18. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
    19. Matsuyama, Kiminori & Sushko, Iryna & Gardini, Laura, 2016. "Revisiting the model of credit cycles with Good and Bad projects," Journal of Economic Theory, Elsevier, vol. 163(C), pages 525-556.
    20. Simone Galperti & Bruno Strulovici, 2017. "A Theory of Intergenerational Altruism," Econometrica, Econometric Society, vol. 85, pages 1175-1218, July.
    21. Makoto Yano & Kenji Sato, 2019. "Ergodic chaos for non‐expansive economic models*," International Journal of Economic Theory, The International Society for Economic Theory, vol. 15(3), pages 311-320, September.
    22. Yuichi Furukawa, 2007. "Endogenous Growth Cycles," Journal of Economics, Springer, vol. 91(1), pages 69-96, May.
    23. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    24. Fujiu Hiroshi & Yano Makoto, 2019. "Two-sided altruism as a motive for intergenerational transfer," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-8, September.
    25. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    26. Ray, Debraj, 1987. "Nonpaternalistic intergenerational altruism," Journal of Economic Theory, Elsevier, vol. 41(1), pages 112-132, February.
    27. Hiroshi Fujiu & Makoto Yano, 2008. "Altruism as a motive for intergenerational transfers," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 95-114, March.
    28. Gardini, Laura & Sushko, Iryna, 2019. "Growing through chaos in the Matsuyama map via subcritical flip bifurcation and bistability," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 52-67.
    29. Dimitrios Varvarigos, 2017. "Endogenous cycles and human capital," Journal of Economics, Springer, vol. 120(1), pages 31-45, January.
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