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Monotonicity and Continuity of the Critical Capital Stock in the Dechert-Nishimura Model

Author

Listed:
  • Ken-Ichi Akao

    (School of Social Sciences, Waseda University, Japan)

  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Kazuo Nishimura

    (KIER, Kyoto University, Japan)

Abstract

We show that the critical capital stock of the Dechert-Nishimura (1983) model is a decreasing and continuous function of the discount factor. We also show that the critical capital stock merges with a nonzero steady state as the discount factor decreases to a certain boundary value, and that the critical capital stock converges to the minimum sustainable capital stock as the discount factor increases to another boundary value.

Suggested Citation

  • Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2011. "Monotonicity and Continuity of the Critical Capital Stock in the Dechert-Nishimura Model," Discussion Paper Series DP2011-20, Research Institute for Economics & Business Administration, Kobe University, revised Sep 2011.
    • Handle: RePEc:kob:dpaper:dp2011-20
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2011-20.pdf
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    Cited by:

    1. Ha-Huy, Thai & Tran, Nhat Thien, 2020. "A simple characterisation for sustained growth," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 141-147.
    2. Sanchez-Carrera Edgar J. & Ille Sebastian & Travaglini Giuseppe, 2021. "Macrodynamic Modeling of Innovation Equilibria and Traps," The B.E. Journal of Macroeconomics, De Gruyter, vol. 21(2), pages 659-694, June.
    3. Cuong Le Van & Çağrı Sağlam & Agah Turan, 2016. "Optimal Growth Strategy under Dynamic Threshold," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(6), pages 979-991, December.
    4. Le Van, Cuong & Pham, Ngoc-Sang & Pham, Thi Kim Cuong, 2021. "Development loans, poverty trap, and economic dynamics," MPRA Paper 110870, University Library of Munich, Germany.
    5. Ha-Huy, Thai & Tran, Nhat-Thien, 2019. "A simple characterization for sustained growth," MPRA Paper 94576, University Library of Munich, Germany.
    6. Le Van, Cuong & Pham, Ngoc-Sang & Pham, Thi Kim Cuong, 2023. "Effects of development aid (grants and loans) on the economic dynamics of the recipient country," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 101-112.
    7. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    8. Sağlam Çağri & Turan Agah & Turan Hamide, 2014. "Saddle-node bifurcations in an optimal growth model with preferences for wealth habit," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(2), pages 145-156, April.
    9. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2015. "Skiba points in free end-time problems," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 404-419.
    10. Crettez, Bertrand & Hayek, Naila & Morhaim, Lisa, 2017. "Optimal growth with investment enhancing labor," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 23-36.
    11. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2025. "Critical capital stock in a continuous-time growth model with a convex-concave production function," Journal of Mathematical Economics, Elsevier, vol. 119(C).

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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