IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v109y2001i2d10.1023_a1017518523055.html
   My bibliography  Save this article

Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions

Author

Listed:
  • N. SAGARA

    (Hosei University)

Abstract

This paper deals with the existence problem of optimal growth with recursive utility in a continuous-time model without convexity assumptions. We consider a general reduced model of capital accumulation and provide an existence result allowing the production technology to be nonconvex and the objective functional to be nonconcave and recursive. The program space under investigation is a weighted Sobolev space with discounting built in, as introduced by Chichilnisky. The compactness of the feasible set and the continuity of the objective are proven by the effective use of ℒ2-convergence. Existence follows from the classical Weierstrass theorem.

Suggested Citation

  • N. Sagara, 2001. "Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 371-383, May.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017518523055
    DOI: 10.1023/A:1017518523055
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1017518523055
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1017518523055?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    2. Russell Davidson & Richard Harris, 1981. "Non-Convexities in Continuous Time Investment Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(2), pages 235-253.
    3. Becker, Robert A. & Boyd, John III & Sung, Bom Yong, 1989. "Recursive utility and optimal capital accumulation. I. Existence," Journal of Economic Theory, Elsevier, vol. 47(1), pages 76-100, February.
    4. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, vol. 55(2), pages 329-355, March.
    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    6. Romer, Paul M, 1986. "Cake Eating, Chattering, and Jumps: Existence Results for Variational Problems," Econometrica, Econometric Society, vol. 54(4), pages 897-908, July.
    7. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    8. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
    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. Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1-2), pages 574-581, January.

    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. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    2. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
    3. Barucci, Emilio & Zezza, Pierluigi, 1996. "Does a life cycle exist for a hedonistic consumer?," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 57-69, August.
    4. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    5. Tom Kompas & Omar Abdel-Razeq, 2001. "A Simple Monetary Growth Model with Variable Rates of Time Preference," International and Development Economics Working Papers idec01-10, International and Development Economics.
    6. Hayakawa, Hiroaki, 1995. "The complete complementarity of consumption and real balances and the strong superneutrality of money," Economics Letters, Elsevier, vol. 48(1), pages 91-97, April.
    7. Ken-ichi Hirose & Shinsuke Ikeda, 2012. "Decreasing marginal impatience in a two-country world economy," Journal of Economics, Springer, vol. 105(3), pages 247-262, April.
    8. Takashi Hayashi, 2020. "Investment in time preference and long-run distribution," The Japanese Economic Review, Springer, vol. 71(2), pages 171-190, April.
    9. Ken-Ichi Hirose & Shinsuke Ikeda, 2015. "Decreasing Marginal Impatience and Capital Accumulation in a Two-Country World Economy," Metroeconomica, Wiley Blackwell, vol. 66(3), pages 474-507, July.
    10. Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1-2), pages 574-581, January.
    11. Been-Lon Chen & Mei Hsu & Chia-Hui Lu, 2008. "Inflation and Growth: Impatience and a Qualitative Equivalence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(6), pages 1309-1323, September.
    12. Wen‐Ya Chang & Hsueh‐Fang Tsai & Wen‐Fang Liu, 1998. "Effects of Government Spending on the Current Account with Endogenous Time Preference," Southern Economic Journal, John Wiley & Sons, vol. 64(3), pages 728-740, January.
    13. Hiroaki Hayakawa, 2020. "Consumer behavior in a monetary economy and smoothing of composite consumption," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 10(1), pages 89-122, March.
    14. Ken-Ichi Hirose & Shinsuke Ikeda, 2013. "Time Preference and Dynamic Stability in an N-Country World Economy," ISER Discussion Paper 0887, Institute of Social and Economic Research, Osaka University.
    15. Meixing Dai, 2007. "Endogenous Wealth-Depending Time Preference and Fiscal Policy in Open Economy," Economics Bulletin, AccessEcon, vol. 8(7), pages 1-7.
    16. Federico Perali & Luca Piccoli, 2022. "An Extended Theory of Rational Addiction," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    17. Gootzeit, Michael & Schneider, Johannes & Smith, William, 2002. "Marshallian recursive preferences and growth," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 381-404, November.
    18. Ken‐Ichi Hirose & Shinsuke Ikeda, 2008. "On Decreasing Marginal Impatience," The Japanese Economic Review, Japanese Economic Association, vol. 59(3), pages 259-274, September.
    19. Hiroaki Hayakawa, 2019. "Time Preferences, Intertemporal Optimization, and the Permanent Income-Life Cycle Hypothesis," Growth, Asian Online Journal Publishing Group, vol. 6(1), pages 1-11.
    20. repec:ebl:ecbull:v:8:y:2007:i:7:p:1-7 is not listed on IDEAS
    21. Hirose, Ken-Ichi & Ikeda, Shinsuke, 2012. "Decreasing and increasing marginal impatience and the terms of trade in an interdependent world economy," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1551-1565.

    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:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017518523055. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.