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Nonlinear functional analysis and optimal economic growth

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  • 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
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    Citations

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    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. Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
    6. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    7. Chichilnisky, Graciela & Beltratti, Andrea & Heal, Geoffrey, 1998. "Sustainable use of renewable resources, Chapter 2.1," MPRA Paper 8815, University Library of Munich, Germany.
    8. 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.
    9. Barucci, Emilio, 2000. "Differential games with nonconvexities and positive spillovers," European Journal of Operational Research, Elsevier, vol. 121(1), pages 193-204, February.
    10. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
    11. 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

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