Application of functional analysis to models of efficient allocation of economic resources |
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| Authors: | G. Chichilnisky P. J. Kalman |
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| Affiliation: | (1) Columbia University, New York;(2) Harvard Institute for International Development, Cambridge, Massachusetts;(3) State University of New York at Stonybrook, New York;(4) Department of Economics, Harvard University, Cambridge, Massachusetts |
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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 of a class of welfare functions (nonlinear operators defined on consumption paths) for continuity in a weightedl2-norm.This research was supported by the National Science Foundation, Grant No. GS-18174. The authors thank K. Arrow, A. Gleason, F. Hahn, A. Majda, S. Marglin, T. Muench, L. Tartar, S. Karamardian, and the referees for helpful comments and suggestions. |
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| Keywords: | Hilbert spaces existence theorems functional analysis applied mathematics |
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