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Application of functional analysis to models of efficient allocation of economic resources

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  • Chichilnisky, Graciela
  • Kalman, P. J.

Abstract

The present paper studies existence and characterization of efficient paths in infinite-horizon economic growth models: the method used is based on techniques of nonlinear functional analysis on Hilbert spaces developed earlier by Chichilnisky. Necessary and sufficient conditions are given for the existence of positive competitive price systems in which the efficient programs maximize present value and intertemporal profit. Approximation of these competitive price systems by strictly positive ones with similar properties is studied. A complete characterization is also given f a class of welfare functions (nonlinear operators defined on consumption paths) for continuity in a weighted L2-norm.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8004.

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Date of creation: 1979
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Publication status: Published in Journal of Optimization Theory and Applications No. 1.30(1980): pp. 19-32
Handle: RePEc:pra:mprapa:8004

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Related research

Keywords: Hilbert spaces; existence theorems; functional analysis; applied mathematics;

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References

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  1. McFadden, Daniel, 1975. "An example of the non-existence of Malinvaud prices in a tight economy," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 17-19, March.
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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. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer, vol. 13(2), pages 231-257, April.
  3. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer, vol. 27(1), pages 1-34, 08.
  4. Chichilnisky, Graciela, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Economics Discussion Papers 2009-8, Kiel Institute for the World Economy.
  5. William R. Zame & Y.A. Abramovich & C.D. Aliprantis, 1994. "A Representation Theorem for Riesz Spaces and its Applications to Economics," UCLA Economics Working Papers 725, UCLA Department of Economics.
  6. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer, vol. 19(1), pages 113-185, March.

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