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 weightedl 2-norm.
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Communicated by S. Karamardian
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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Chichilnisky, G., Kalman, P.J. Application of functional analysis to models of efficient allocation of economic resources. J Optim Theory Appl 30, 19–32 (1980). https://doi.org/10.1007/BF00934586
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DOI: https://doi.org/10.1007/BF00934586