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Existence of an optimal path in a continuous-time nonconcave Ramsey model

Author

Listed:
  • Ken-Ichi Akao

    (School of Social Sciences, Waseda University, 1-6-1 Nishiwaseda Shinjuku Tokyo, 169-8050, Japan.)

  • Hitoshi Ishii

    (Institute for Mathematics and Computer Science, Tsuda College.)

  • Takashi Kamihigashi

    (Research Institute for Economics and Business Administration, Kobe University, Japan.)

  • Kazuo Nishimura

    (Research Institute for Economics and Business Administration, Kobe University, Japan.)

Abstract

We show an existence theorem for a continuous-time nonconcave Ramsey model. In existing existence theorems, a bounded condition is required to ensure the compactness of the set of feasible control paths. Although our existence theorem is for a specific Ramsey model, it does not require such a bounded condition. The continuous-time Ramsey model is extensively used. In many cases, the analysis has been conducted without explicit reference to the conditions for the existence of an optimal path or simply by assuming its existence. Our result provides validity to such analyses.

Suggested Citation

  • Ken-Ichi Akao & Hitoshi Ishii & Takashi Kamihigashi & Kazuo Nishimura, 2019. "Existence of an optimal path in a continuous-time nonconcave Ramsey model," RIEEM Discussion Paper Series 1905, Research Institute for Environmental Economics and Management, Waseda University.
    • Handle: RePEc:was:dpaper:1905
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    References listed on IDEAS

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    1. Hippolyte d’Albis & Pascal Gourdel & Cuong Le Van, 2008. "Existence of solutions in continuous-time optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 321-333, November.
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    3. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    4. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2019. "Optimal steady state of an economic dynamics model with a nonconcave production function," RIEEM Discussion Paper Series 1907, Research Institute for Environmental Economics and Management, Waseda University.
    5. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.
    6. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, November.
    7. Takashi Kamihigashi & Santanu Roy, 2006. "Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 325-340, October.
    8. Graciela Chichilnisky, 1981. "Existence and Characterization of Optimal Growth Paths Including Models with Non-Convexities in Utilities and Technologies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 51-61.
    9. Romer, Paul M, 1986. "Cake Eating, Chattering, and Jumps: Existence Results for Variational Problems," Econometrica, Econometric Society, vol. 54(4), pages 897-908, July.
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    Cited by:

    1. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.

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    More about this item

    Keywords

    Continuous-time nonconcave Ramsey model; existence of an optimal path;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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