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Nonlinear functional analysis and optimal economic growth


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  • Chichilnisky, Graciela


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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7990.

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Date of creation: 1977
Date of revision:
Publication status: Published in Journal of Mathematical Analysis and Applications no. 2.61(1977): pp. 504-520
Handle: RePEc:pra:mprapa:7990

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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;

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Cited by:
  1. Chichilnisky, Graciela & Gruenwald, Paul F., 1994. "Existence of an optimal growth path with endogenous technical change," MPRA Paper 8394, University Library of Munich, Germany.
  2. Chichilnisky, G & Zhou, Y, 1996. "Smooth Infinite Economiesq," Discussion Papers, Columbia University, Department of Economics 1996_30, Columbia University, Department of Economics.
  3. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer, Springer, vol. 32(3), pages 497-509, September.
  4. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
  5. Graciela Chichilnisky, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Working Papers, LAMETA, Universtiy of Montpellier 09-07, LAMETA, Universtiy of Montpellier, revised Aug 2009.
  6. Barucci, Emilio & Zezza, Pierluigi, 1996. "Does a life cycle exist for a hedonistic consumer?," Mathematical Social Sciences, Elsevier, Elsevier, vol. 32(1), pages 57-69, August.
  7. repec:hal:journl:halshs-00197546 is not listed on IDEAS
  8. Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
  9. Chichilnisky, Graciela & Beltratti, Andrea & Heal, Geoffrey, 1998. "Sustainable use of renewable resources, Chapter 2.1," MPRA Paper 8815, University Library of Munich, Germany.
  10. repec:hal:journl:halshs-00101140 is not listed on IDEAS


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