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A multidimensional, nonconvex model of optimal growth

Author

Listed:
  • Stefano Bosi

    (Université Paris-Saclay, Univ Evry, EPEE)

  • Thai Ha-Hui

    (Université Paris-Saclay, Univ Evry, EPEE)

Abstract

In this article, we consider a multidimensional economy where the standard supermodularity property fails. We generalize the notion of net gain of investment, introduced by Kamihigashi and Roy [7] and applied to one-sector growth models, to the case of multiple capital stocks. We prove the convergence to the set of steady states without relying on the monotonicity of optimal path. Our approach differs from the standard dynamic programming based on convexity or supermodularity. We find that preferences are key to shape the economy in the long run.

Suggested Citation

  • Stefano Bosi & Thai Ha-Hui, 2023. "A multidimensional, nonconvex model of optimal growth," Documents de recherche 23-07, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    • Handle: RePEc:eve:wpaper:23-07
    as

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    File URL: https://www.univ-evry.fr/fileadmin/mediatheque/ueve-institutionnel/03_Recherche/laboratoires/Epee/pub/WorkingPapers_CEPS_7.pdf
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    References listed on IDEAS

    as
    1. Dam, My & Ha-Huy, Thai & Le Van, Cuong & Nguyen, Thi Tuyet Mai, 2020. "Economic dynamics with renewable resources and pollution," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 14-26.
    2. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    3. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    4. N. Hung & C. Le Van & P. Michel, 2009. "Non-convex aggregate technology and optimal economic growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 457-471, September.
    5. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    6. repec:hal:cesptp:hal-03261262 is not listed on IDEAS
    7. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    8. Montrucchio, Luigi & Sorger, Gerhard, 1996. "Topological entropy of policy functions in concave dynamic optimization models," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 181-194.
    9. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    10. repec:hal:journl:hal-03261262 is not listed on IDEAS
    11. repec:hal:pseptp:hal-03261262 is not listed on IDEAS
    12. Kazuo Nishimura & John Stachurski, 2012. "Stability of Stochastic Optimal Growth Models: A New Approach," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 289-307, Springer.
    13. 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.
    14. Mukul Majumdar & Tapan Mitra, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 143-151.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    net gain of investment; multidimensional economy; nonconvexities;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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