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

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Author Info
Chichilnisky, Graciela
Kalman, P. J.

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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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File URL: http://mpra.ub.uni-muenchen.de/8004/
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Publisher 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;

Find related papers by JEL classification:
D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium

References listed on IDEAS
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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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer, vol. 27(1), pages 1-34, 08. [Downloadable!] (restricted)
  2. Chichilnisky, Graciela & Gruenwald, Paul F., 1994. "Existence of an optimal growth path with endogenous technical change," MPRA Paper 8394, University Library of Munich, Germany. [Downloadable!]
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  3. 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. [Downloadable!]
    Other versions:
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