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Existence of Solutions in Continuous-time Optimal Growth Models

Author

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  • Hippolyte d'Albis

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Pascal Gourdel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.

Suggested Citation

  • Hippolyte d'Albis & Pascal Gourdel & Cuong Le Van, 2008. "Existence of Solutions in Continuous-time Optimal Growth Models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00177269, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00177269
    DOI: 10.1007/s00199-007-0294-8
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00177269
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    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    3. HILDENBRAND, Werner & MERTENS, Jean-François, 1971. "On Fatou's lemma in several dimensions," LIDAM Reprints CORE 72, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Magill, Michael J P, 1981. "Infinite Horizon Programs," Econometrica, Econometric Society, vol. 49(3), pages 679-711, May.
    5. 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.
    6. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    7. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    8. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Groth, Christian & Ricci, Francesco, 2011. "Optimal growth when environmental quality is a research asset," Research in Economics, Elsevier, vol. 65(4), pages 340-352, December.
    4. Le, Thanh & Le Van, Cuong, 2016. "Transitional dynamics in an R&D-based growth model with natural resources," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 1-17.
    5. Aditya Goenka & Lin Liu, 2020. "Infectious diseases, human capital and economic growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 1-47, July.
    6. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    7. Manh Hung Nguyen & Phu Nguyen Van, 2008. "Growth and convergence in a model with renewable and nonrenewable resources," Working Papers 21, Development and Policies Research Center (DEPOCEN), Vietnam.
    8. 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.
    9. Nguyen, Manh-Hung & Nguyen-Van, Phu, 2010. "Growth and convergence in a model with renewable and non-renewable resources: existence, transitional dynamics, and empirical evidence," TSE Working Papers 10-210, Toulouse School of Economics (TSE).
    10. Zachariah Sinkala & Vajira Manathunga & Bichaka Fayissa, 2022. "An Epidemic Compartment Model for Economic Policy Directions for Managing Future Pandemic," Papers 2202.05374, arXiv.org.

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    More about this item

    Keywords

    optimization; continuous time; optimal growth;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical

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