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Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth

Author

Listed:
  • Liuchun Deng

    (Yale-NUS College)

  • Minako Fujio

    (Yokohama National University)

  • M. Ali Khan

    (The Johns Hopkins University)

Abstract

This paper investigates the well-known phenomenon of eventual periodicity of Li–Yorke chaos in the context of the two-sector Robinson–Shinkai–Leontief model of economic growth. It locates its (i) presence under specific parameter restrictions that include the extreme classical saving specification, and its (ii) absence in savings generated by the optimization of an infinitely-lived representative agent with perfect foresight. These results in which rare events, chaos and stability are all brought together under the rubric of upward and downward inertia, while of substantive economic interest of their own, also highlight phenomena in economic dynamics that may go towards a clearer definitional understanding of chaotic systems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:72:y:2021:i:2:d:10.1007_s00199-020-01301-0
    DOI: 10.1007/s00199-020-01301-0
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    Cited by:

    1. Hashimoto, Ken-ichi & Im, Ryonghun & Kunieda, Takuma & Shibata, Akihisa, 2022. "Financial destabilization," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. 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.
    3. Liuchun Deng & Minako Fujio & M. Ali Khan, 2023. "On optimal extinction in the matchbox two-sector model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 445-494, August.
    4. 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.
    5. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2022. "Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos," Journal of Economic Theory, Elsevier, vol. 201(C).

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    More about this item

    Keywords

    Two-sector model; Equilibrium growth; Optimum growth; Eventual periodicity; Chaos;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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