I examine optimal monetary policy in a Lagos and Wright [A unified framework for monetary theory and policy analysis, J. Polit. Econ. 113 (2005) 463—484] model where trade is centralized and all exchange is voluntary. I identify a class of incentive feasible policies that improve welfare beyond what is achievable with zero intervention. Any policy in this class necessarily entails a non-negative inflation rate and a strictly positive nominal interest rate. Despite the absence of a lump-sum tax instrument, there exists an incentive-feasible policy that implements the first-best allocation.
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