Examples of Excess Demand Functions on Infinite-Dimensional Commodity Spaces
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The Walrasian equilibrium problem with a finite dimensional commodity space has been studied rather extensively in the past. The existence of equilibrium prices in economies with a finite dimensional commodity space has been demonstrated very satisfactorily; see [8,9]. However, a number of economic situations lead naturally to infinite dimensional commodity spaces. In such a case, the mathematical tools employed in the finite dimensional case do not yield similar equilibrium results. Due to the nature of infinite dimensional spaces, questions about compactness of budget sets, continuity of utility and excess demand functions, utility maximization problems, etc. are very subtle. For this very reason, there are no satisfactory results guaranteeing the existence of equilibrium prices in economies with infinite dimensional commodity spaces. However, in spite of these difficulties, considerable progress has been made on the equilibrium problem with infinite dimensional commodity spaces.
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- 2.C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York — London, 1978.Google Scholar
- 3.C.D. Aliprantis and O. Burkinshaw, positive Operators, Academic Press. (In press, to appear in 1985.)Google Scholar
- 5.P. Bojan, A generalization of theorems on the existence of competitive economic equilibrium in the case of infinitely many commodities, Math. Balkanica 4(1974), 491–494.Google Scholar
- 7.G. Chichilnisky and G. Heal, Existence of competitive equilibrium in Hilbert spaces, Institute for Mathematics and its Applications-University of Minnesota, Preprint # 79, 1984.Google Scholar
- 8.G. Debreu, Theory of Value, John Wiley, New York, 1959.Google Scholar
- 9.G. Debreu, Existence of competitive equilibrium. In: M. Intriligator and K. Arrow Eds., Handbook of Mathematical Economics, Vol. II, Chapter 15, pp. 697–743, North-Holland, Amsterdam, 1982.Google Scholar
- 12.L. Jones, Special problems arising in the theory of economies with infinitely many commodities, The center for mathematical studies in economics and management science, Northwestern University, Discussion Paper #596, 1984.Google Scholar
- 13.L. Jones, A note on the price equilibrium existence problem in Banach lattices, The center for mathematical studies in economics and management science, Northwestern University, Discussion Paper # 600, 1984.Google Scholar
- 16.W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.Google Scholar
- 18.A. Mas-Colell, The price equilibrium problem in Banach lattices, Harvard University Discussion Paper, 1983.Google Scholar
- 22.N. C. Yannelis, On a market equilibrium theorem with an infinite number of commodities, J. Math. Analysis and Applications, forthcoming.Google Scholar
- 23.N. C. Yannelis and W. R. ZAME, Equilibria in Banach lattices without ordered preference, Institute for Mathematics and its Applications-University of Minnesota, Preprint # 71, 1984.Google Scholar