This paper develops a dynamic model of seigniorage in which economies' equilibrium paths reflect the ongoing strategic interaction between an optimizing government and a rational public. The model extends existing positive models of monetary policy and inflation by explicitly incorporating the intertemporal linkages among budget deficits, debt, and inflation. A central finding is that the public's rational responses to government policies may well create incentives for the government to reduce inflation and the public debt over time. A sufficiently myopic government may, however, provoke a rising equilibrium path of inflation and public debt.