Advances in Equilibrium Theory pp 131-143 | Cite as

# Examples of Excess Demand Functions on Infinite-Dimensional Commodity Spaces

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## Abstract

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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## References

- 1.C.D. Aliprantis and D.J. Brown, Equilibria in markets with a Riesz space of commodities,
*J. Math, Economics*11(1983), 189–207.CrossRefGoogle Scholar - 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 - 4.T. F. Bewley, Existence of equilibrium in economies with infinitely many commodities,
*J. Economic Theory*4(1972), 514–540.CrossRefGoogle 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 - 6.D. J. Brown and L. M. Lewis, Myopic economic agents,
*Econometrica*49(1981), 359–368.CrossRefGoogle 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 - 10.M. Florenzano, On the existence of equilibria in economies with an infinite dimensional commodity space,
*J. Math. Economics*12(1983), 233–245.CrossRefGoogle Scholar - 11.L. JONES, Existence of equilibria with infinitely many consumers and infinitely many commodities: A theorem based on models of commodity differentiation,
*J. Math. Economics*12(1983), 119–138.CrossRefGoogle 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
- 14.A. M. Khan, A remark on the existence of equilibrium in markets without ordered preferences and with a Riesz space of commodities,
*J. Math. Economics*13(1984), 165–169.CrossRefGoogle Scholar - 15.D.M. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities,
*J. Math. Economlas*2(1981), 15–35.CrossRefGoogle Scholar - 16.W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I,
*North-Holland*, Amsterdam, 1971.Google Scholar - 17.A. Mas-Colell, A model of equilibrium with differentiated commodities,
*J. Math. Economies 2*(1975), 263–295.CrossRefGoogle Scholar - 18.A. Mas-Colell, The price equilibrium problem in Banach lattices, Harvard University Discussion Paper, 1983.Google Scholar
- 19.J. M. Ostroy, On the existence of Walrasian equilibrium in large-square economies,
*J. Math. Economics*13(1984), 143–163.CrossRefGoogle Scholar - 20.H. H. Schaefer, Banach Lattices and Positive Operators,
*Springer-Verlag*, New York — Heidelberg, 1974.CrossRefGoogle Scholar - 21.S. Toussaint, On the existence of equilibria in economies with infinitely many commodities and without ordered preferences,
*J. Economic Theory*33(1984), 98–115.CrossRefGoogle 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