This paper studies the interactions of fiscal policy and monetary policy when they stabilize a single economy against shocks in a dynamic setting. If both policy-makers are benevolent, then, in our model, the best outcome is achieved when monetary policy does nearly all of the stabilization. If the monetary authorities are benevolent, but the fiscal authority discounts the future, or aims for an excessive level of output, then a Nash equilibrium will result in large welfare losses: after an inflation shock there will be excessively tight monetary policy, excessive fiscal expansion, and a rapid accumulation of public debt. However, if, in these circumstances, there is a regime of fiscal leadership, then the outcome will be very nearly as good as when both policy-makers are benevolent.