Chichilnisky, Graciela and Kalman, P. J. (1979): Application of functional analysis to models of efficient allocation of economic resources. Published in: Journal of Optimization Theory and Applications , Vol. 30, No. No. 1 (January 1980): pp. 19-32.
Download (1877Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Application of functional analysis to models of efficient allocation of economic resources|
|Keywords:||Hilbert spaces; existence theorems; functional analysis; applied mathematics|
|Subjects:||D - Microeconomics > D6 - Welfare Economics > D61 - Allocative Efficiency; Cost-Benefit Analysis
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||31. Mar 2008 05:39|
|Last Modified:||12. Feb 2013 14:04|
N. DUNFORD AND J. SCHWARTZ, "Linear Operators," Interscience, New York, 1958.
K.J. ARROW, E. W. BARANKIN, AND D. BLACKWELL., Admissible points in convex sets, in "Contributions to the Theory of Games" (H. W. Kuhn and A.W. Tucker, Eds.), Vol. II, pp. 87-92, Princeton Univ. Press, Princeton, N.J., 1953.
RADNER, R., On maximal points in convex sets, Proceedings of the Fifth Berkeley Symposium on Probability and Statistics. Univ. of Cali. Press, Berkeley, CA, 1965.
G. CHICHILNISKY, Nonlinear functional analysis and optimal economic growth, J. Math. Anal. Vol. 61 (1977), 504-520.
RADNER, R., AND MAJUMDAR, M., Shadow prices for infinite growth programs: The functional analysis approach, Techniques of optimization, Edited by A. V. Blakrishnan. Academic Press, New York, 1972.
MALINVAUD, E., Capital accumulation and efficient allocation of resources, Econometrica, Vol. 21, pp. 253-276, 1953.
G. DEBREU, Valuation Equilibrium and Pareto Optimum, Proc. Nat. Acad. Sci. (1954).
KELLEY, J., AND NAMIOKA, I., Linear topological spaces, D. Van Norstrand Company, New York, 1963.
PELEG, B., On competitive prices for optima consumption plans, SIAM Journal on Applied Mathematics, Vol 26, pp. 239-253, 1974.
MCFADDEN, D., An example of the non-existence of Malinvaud prices in a tight economy, Journal of Math. Econ., Vol. 2, pp.17-19, 1975.
M. A. KRASNOSEL'SKII, "Topological Methods in the Theory of Nonlinear Integral Equations," Macmillan CO., New York, 1964.