Singularities, Walrasian economies and economic crisis
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We consider pure exchange economies whose consumption spaces are Banach lattices. The utility functions are strictly concave, Gateaux differentiable, and not necessarily separable. Following the Negishi approach and using the excess utility function, we introduce a notion of social equilibria. We show that there exists a bijective correspondence between this set and the set of Walrasian equilibria. By transforming the problem of finding the Walrasian equilibria into an equivalent problem of finding social equilibria, we can use techniques of smooth functional analysis to show that a suitable large subset of economies are regular and its equilibrium set is a Banach manifold. Finally, we focus on the complement of this set, i.e. the set of singular economies, and we analyze its main characteristics, among them, those that are the causes of economic crises. © SpringerVerlag Berlin Heidelberg 2011.
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Economic crisis; Equilibrium sets; Pure exchanges; Utility functions; Banach spaces
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