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Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems

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  • Mitra, Tapan
  • Nishimura, Kazuo

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  • Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    • Handle: RePEc:eee:jetheo:v:96:y:2001:i:1-2:p:256-293
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    10. Deneckere, Raymond & Pelikan, Steve, 1986. "Competitive chaos," Journal of Economic Theory, Elsevier, vol. 40(1), pages 13-25, October.
    11. Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 649-676, August.
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    13. Kazuo Nishimura & Makoto Yano, 2012. "Non-linear Dynamics and Chaos in Optimal Growth: An Example," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 127-150, Springer.
    14. Dutta, Prajit K. & Mitra, Tapan, 1989. "Maximum theorems for convex structures with an application to the theory of optimal intertemporal allocation," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 77-86, February.
    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. Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
    17. 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.
    18. Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 705-717, August.
    19. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
    20. McKenzie, Lionel W., 1983. "Turnpike theory, discounted utility, and the von Neumann facet," Journal of Economic Theory, Elsevier, vol. 30(2), pages 330-352, August.
    21. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    22. McKenzie, Lionel W., 1982. "A primal route to the Turnpike and Liapounov stability," Journal of Economic Theory, Elsevier, vol. 27(1), pages 194-209, June.
    23. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    24. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
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    Cited by:

    1. K. Nishimura & H. Takahashi & A. Venditti, 2006. "Endogenous Fluctuations in Two-Sector Models: Role of Preferences," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 309-331, February.
    2. Kazuya Kamiya & Takashi Shimizu, 2010. "Hysteresis in Dynamic General Equilibrium Models with Cash-in-Advance Constraints," CIRJE F-Series CIRJE-F-765, CIRJE, Faculty of Economics, University of Tokyo.
    3. Ghiglino, Christian & Venditti, Alain, 2007. "Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies," Journal of Economic Theory, Elsevier, vol. 135(1), pages 414-441, July.
    4. Bella, Giovanni, 2017. "Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 452-460.
    5. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    6. Ghiglino, Christian & Venditti, Alain, 2011. "Wealth distribution and output fluctuations," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2478-2509.
    7. 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.
    8. Roberto Cominetti & Adriana Piazza, 2009. "Asymptotic Convergence of Optimal Policies for Resource Management with Application to Harvesting of Multiple Species Forest," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 576-593, August.
    9. Orlando Gomes, 2006. "Local Bifurcations and Global Dynamics in a Solow-type Endogenous Business Cycles Model," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 91-127, May.
    10. Adriana Piazza, 2009. "The optimal harvesting problem with a land market: a characterization of the asymptotic convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 113-138, July.
    11. Stefano Bosi & Francesco Magris & Alain Venditti, 2003. "Indeterminacy in a Cash-in-Advance Two-Sector Economy," Documents de recherche 03-04, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    12. Tarek Coury & Yi Wen, 2007. "Global indeterminacy in locally determinate RBC models," Working Papers 2007-029, Federal Reserve Bank of St. Louis.
    13. Christian Ghiglino & Alain Venditti, 2008. "The role of the wealth distribution on output volatility," Working Papers halshs-00281379, HAL.
    14. Mitra, Tapan & Nishimura, Kazuo, 2001. "Introduction to Intertemporal Equilibrium Theory: Indeterminacy, Bifurcations, and Stability," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 1-12, January.
    15. Dasgupta, Swapan & Mitra, Tapan, 2010. "On Optimal Forest Management: A Bifurcation Analysis," Working Papers 10-04, Cornell University, Center for Analytic Economics.
    16. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.
    17. Tapan Mitra, 2005. "Characterization of the turnpike property of optimal paths in the aggregative model of intertemporal allocation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(4), pages 247-275, December.

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