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Voluntary and Efficient Allocations are Walrasian
Joaquim Silvestre
Abstract
Let E be a private ownership economy. Call an allocation w "voluntary for a price vector p" if no agent can benefit by trading less at p. We prove that, under differentiability and interiority, if w is voluntary and Pareto efficient it is a competitive equilibrium for E. Perhaps surprisingly, production economies where some agents receive profit income require a stronger voluntariness condition than the one sufficient for exchange economies. The stronger condition singles out a commodity as a medium of exchange.
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