IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00177269.html
   My bibliography  Save this paper

Existence of Solutions in Continuous-time Optimal Growth Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00177269/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00199-007-0294-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    9. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    2. ?gel de la Fuente, "undated". "Convergence Across Countries And Regions: Theory And Empirics," UFAE and IAE Working Papers 447.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Alejandro Diaz-Bautista, 2005. "Regional Convergence of Income and Labor Productivity in Mexico," Urban/Regional 0512016, University Library of Munich, Germany.
    4. repec:ebl:ecbull:v:2:y:2002:i:1:p:1-15 is not listed on IDEAS
    5. Acemoglu, Daron & Johnson, Simon & Robinson, James A., 2005. "Institutions as a Fundamental Cause of Long-Run Growth," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 6, pages 385-472, Elsevier.
    6. Gomes, Orlando, 2007. "Externalities in R&D: a route to endogenous fluctuations," MPRA Paper 2850, University Library of Munich, Germany.
    7. Robert J. Barro & Xavier Sala-I-Martin, 1992. "Public Finance in Models of Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 645-661.
    8. Xiangcai Meng & Azhong Ye, 2009. "Human Capital Externality, Knowledge Spillover, and Sustainable Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 10(1), pages 155-198, May.
    9. repec:ebl:ecbull:v:15:y:2007:i:8:p:1-7 is not listed on IDEAS
    10. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 103-126, October.
    11. Ben-David, Dan & Loewy, Michael B, 1998. "Free Trade, Growth, and Convergence," Journal of Economic Growth, Springer, vol. 3(2), pages 143-170, June.
    12. Cem Ertur & Thiaw Kalidou, 2005. "Growth and Spatial Dependence - The Mankiw, Romer and Weil model revisited," ERSA conference papers ersa05p660, European Regional Science Association.
    13. Aykut Kibritçioglu, 2002. "On the Smithian origins of "new" trade and growth theories," Economics Bulletin, AccessEcon, vol. 2(1), pages 1-15.
    14. Galimberti, Jaqueson K., 2009. "Conditioned Export-Led Growth Hypothesis: A Panel Threshold Regressions Approach," MPRA Paper 13417, University Library of Munich, Germany.
    15. Robert J. Barro, 1991. "A Cross-Country Study of Growth, Saving, and Government," NBER Chapters, in: National Saving and Economic Performance, pages 271-304, National Bureau of Economic Research, Inc.
    16. Farshid Mojaver, 2004. "Growth with work ethics," ICER Working Papers 14-2004, ICER - International Centre for Economic Research.
    17. Charles R. Hulten, 1996. "Quality Change in Capital Goods and Its Impact on Economic Growth," NBER Working Papers 5569, National Bureau of Economic Research, Inc.
    18. Daniele Schilirò, 2019. "The Growth Conundrum: Paul Romer’s Endogenous Growth," International Business Research, Canadian Center of Science and Education, vol. 12(10), pages 75-85, October.
    19. Bennett T. McCallum, 1996. "Neoclassical vs. endogenous growth analysis: an overview," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 41-71.
    20. Johan Lundberg, 2006. "Using spatial econometrics to analyse local growth in Sweden," Regional Studies, Taylor & Francis Journals, vol. 40(3), pages 303-316.
    21. Charles R. Hulten, 2000. "Total Factor Productivity: A Short Biography," NBER Working Papers 7471, National Bureau of Economic Research, Inc.
    22. ERREYGERS, Guido & FEREDE, Tadele, 2009. "The end of subsistence farming: Growth dynamics and investments in human and environmental capital in rural Ethiopia," Working Papers 2009008, University of Antwerp, Faculty of Business and Economics.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00177269. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.