This paper applies new computational methods for studying nonstationary dynamics to reevaluate the welfare cost of inflation. A dynamic stochastic general equilibrium model with heterogeneous agents is studied. Incomplete markets induce agents to hold a fiat currency as insurance against idiosyncratic income fluctuations. Rather than comparing steady state equilibria, I measure the welfare cost of inflation by explicitly modeling the transitional dynamics that arise following a change in monetary policy. Transitional dynamics are shown to increase the welfare cost of inflation substantially. Also, contrary to conventional wisdom, transitional dynamic effects are shown to increase the benefits of reducing the inflation rate.