Voluntary and Efficient Allocations are Walrasian - Silvestre, Joaquim (Econometrica, 1985)
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.