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.
Research supported in part by NSF grant DMS 83–19594.
Research supported in part by NSF grant SES 83–96111.
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References
C.D. Aliprantis and D.J. Brown, Equilibria in markets with a Riesz space of commodities, J. Math, Economics 11(1983), 189–207.
C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York — London, 1978.
C.D. Aliprantis and O. Burkinshaw, positive Operators, Academic Press. (In press, to appear in 1985.)
T. F. Bewley, Existence of equilibrium in economies with infinitely many commodities, J. Economic Theory 4(1972), 514–540.
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.
D. J. Brown and L. M. Lewis, Myopic economic agents, Econometrica 49(1981), 359–368.
G. Chichilnisky and G. Heal, Existence of competitive equilibrium in Hilbert spaces, Institute for Mathematics and its Applications-University of Minnesota, Preprint # 79, 1984.
G. Debreu, Theory of Value, John Wiley, New York, 1959.
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.
M. Florenzano, On the existence of equilibria in economies with an infinite dimensional commodity space, J. Math. Economics 12(1983), 233–245.
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.
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.
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.
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.
D.M. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities, J. Math. Economlas 2(1981), 15–35.
W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.
A. Mas-Colell, A model of equilibrium with differentiated commodities, J. Math. Economies 2 (1975), 263–295.
A. Mas-Colell, The price equilibrium problem in Banach lattices, Harvard University Discussion Paper, 1983.
J. M. Ostroy, On the existence of Walrasian equilibrium in large-square economies, J. Math. Economics 13(1984), 143–163.
H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, New York — Heidelberg, 1974.
S. Toussaint, On the existence of equilibria in economies with infinitely many commodities and without ordered preferences, J. Economic Theory 33(1984), 98–115.
N. C. Yannelis, On a market equilibrium theorem with an infinite number of commodities, J. Math. Analysis and Applications, forthcoming.
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.
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Aliprantis, C.D., Brown, D.J., Burkinshaw, O. (1985). Examples of Excess Demand Functions on Infinite-Dimensional Commodity Spaces. In: Aliprantis, C.D., Burkinshaw, O., Rothman, N.J. (eds) Advances in Equilibrium Theory. Lecture Notes in Economics and Mathematical Systems, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51602-3_7
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