IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/7990.html
   My bibliography  Save this paper

Nonlinear functional analysis and optimal economic growth

Author

Listed:
  • Chichilnisky, Graciela

Abstract

A problem of existence and characterization of solutions of optimal growth models in many sector economies is studied The social utility to be optimized is a generalized form of a preference depending additively on consumption at the different dates of the planning period. The optimization b rattrirted to a set of admissible growth paths defined by production-investment-consumption relations described by a system of differential equations. Sufficient conditions are given for existence of a solution in a Hilbert space of paths, without convexity assumptions on either the utilities of the technology, using techniques of nonlinear functional analysis. A characterization is given of the utilities which re continuous with respect to the Hilbert space norm. Under convexity assumptions a characteristic is also given of optimal and efficient solutions by competitive prices.

Suggested Citation

  • Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7990
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/7990/1/MPRA_paper_7990.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
    2. Chichilnisky, Graciela & Gruenwald, Paul F., 1995. "Existence of an optimal growth path with endogenous technical change," Economics Letters, Elsevier, vol. 48(3-4), pages 433-439, June.
    3. 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.
    4. Chichilnisky, Graciela, 2011. "Catastrophic Risks with Finite or Infinite States," MPRA Paper 88760, University Library of Munich, Germany.
    5. Mahdi Ebrahimi Kahou & James Yu & Jesse Perla & Geoff Pleiss, 2024. "How Inductive Bias in Machine Learning Aligns with Optimality in Economic Dynamics," Papers 2406.01898, arXiv.org, revised Jun 2024.
    6. Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
    7. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    8. Chichilnisky, Graciela & Beltratti, Andrea & Heal, Geoffrey, 1998. "Sustainable use of renewable resources, Chapter 2.1," MPRA Paper 8815, University Library of Munich, Germany.
    9. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-25.
    10. Barucci, Emilio, 2000. "Differential games with nonconvexities and positive spillovers," European Journal of Operational Research, Elsevier, vol. 121(1), pages 193-204, February.
    11. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
    12. 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.

    More about this item

    Keywords

    nonlinear; optimal; growth; growth models; many sector; utility; optimization; growth paths; admissible; Hilbert; intertemporal allocations; policy; welfare; social welfare; competitive; topology; Sobolev; feasible; matrix; consumption; Lemmas;
    All these keywords.

    JEL classification:

    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:pra:mprapa:7990. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.