Essential interest-bearing money

I examine optimal monetary policy in a Lagos and Wright [R. Lagos, R. Wright, A unified framework for monetary theory and policy analysis, J. Polit. Economy 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.