Faced with real and nominal shocks, what should a benevolent central bank do, fix the money growth rate or target the inflation rate? In this paper, we make a first attempt at studying the optimal choice of monetary policy instruments in a micro-founded model of money. Specifically, we produce an overlapping generations economy in which limited communication and stochastic relocation creates an endogenous transactions role for fiat money. We find that when the shocks are real, welfare is higher under money growth targeting; when the shocks are nominal and not large, welfare is higher under inflation rate targeting. While under inflation rate targeting, it is always optimal to pursue an expansionary policy, it is never optimal to do so under money growth targeting.