Voluntary and Efficient Allocations are Walrasian
证明，在可微性和内部性条件下，如果一种配置是自愿且帕累托有效的，那么它就是竞争均衡。对于存在利润收入的私人所有制经济，需要更强的自愿性条件，该条件将一种商品指定为交换媒介。
Let F be a private ownership economy. Call an allocation w 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 W. 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.