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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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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