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A classification approach to Walrasian equilibrium with substitutability

Yang, Yi-You (2013): A classification approach to Walrasian equilibrium with substitutability.

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In exchange economies with indivisible objects, the substitutability of agents' preferences is essential for the guaranteed existence of Walrasian equilibrium. In this paper, we analyze the ranges of variation for agents' preferences that will guarantee the existence of equilibrium when some agents' preferences are known to satisfy the substitutability condition. Our approach is based on a classification result that partitions the set of economies into disjoint weak similarity classes such that whenever a weak similarity class contains an economy with an equilibrium, each economy in this class also has an equilibrium. The links among economies in the same weak similarity class are established with the notion of monotonization and tax systems.

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