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Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference

Author

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  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Exeter Business School - University of Exeter, VCREME - Van Xuan Center of Research in Economics, Management and Environment, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Cagri Saglam

    (Bilkent University [Ankara])

  • Selman Erol

    (Bilkent University [Ankara])

Abstract

To account for the development patterns that differ considerably among economies in the long run, a variety of one-sector models that incorporate some degree of market imperfections based on technological external effects and increasing returns have been presented. This paper studies the dynamic implications of, yet another mechanism, the endogenous rate of time preference depending on the stock of capital, in a one-sector growth model. The planner's problem is presented and the optimal paths are characterized. We show that development or poverty traps can arise even under a strictly convex technology. We also show that even under a convex-concave technology, the optimal path can exhibit global convergence to a unique stationary point. The multipliers system associated with an optimal path is proven to be the supporting price system of a competitive equilibrium under externality and detailed results concerning the properties of optimal (equilibrium) paths are provided. We show that the model exhibits globally monotone capital sequences yielding a richer set of potential dynamics than the classic model with exogenous discounting.

Suggested Citation

  • Cuong Le Van & Cagri Saglam & Selman Erol, 2011. "Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639731, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00639731
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00639731
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    Cited by:

    1. 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).
    2. Crettez, Bertrand & Morhaim, Lisa, 2012. "Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 197-206.
    3. Taketo Kawagishi & Kazuo Mino, 2012. "Time Preference and Long-Run Growth: the Role of Patience Capital," Economics Bulletin, AccessEcon, vol. 32(4), pages 3243-3249.
    4. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series 2013/01, European University at St. Petersburg, Department of Economics.
    5. Jean-Michel Grandmont, 2013. "Tribute to Cuong Le Van," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 5-10, March.
    6. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
    7. Camacho, Carmen & Saglam, Cagri & Turan, Agah, 2013. "Strategic interaction and dynamics under endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 291-301.
    8. Luis Alcalá & Fernando Tohmé & Carlos Dabús, 2019. "Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience," Dynamic Games and Applications, Springer, vol. 9(2), pages 314-365, June.
    9. Borissov, Kirill, 2013. "Growth and distribution in a model with endogenous time preferences and borrowing constraints," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 117-128.

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    More about this item

    Keywords

    Endogenous time preference; Optimal growth; Competitive equilibrium; Multiple steady-states;
    All these keywords.

    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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