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Exchange economies in which preferences of some consumers are possibly satiated are considered. In a general model of an atomless exchange economy, the equivalence between the 'Rejective' core and the set of dividend equilibrium allocations is proved by applying Liapunov's theorem in multi-dimensions. In general equilibrium theory, non-satiation of consumers' preferences is an essential assumption and is used in proving the existence of the competitive equilibrium and the equivalence between the core and the competitive equilibrium.
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