We study a model where monetary and fiscal policy share the task of stabilizing output and inflation, and the central bank has been assigned a mandate for the latter. The optimal fiscal policy does not imply assigning to the government a (symmetric) mandate to stabilize output. Instead, the optimal response to the aggregate demnd and supply shocks may be characterized as equivalent to an automatic stabilizer. An alternative but equivalent characterization of fiscal policy is that the government should maximize a "model" social welfarefunction, respectively over (under) weighting the objective of price stability versus output stability when the relative size of aggregate demand vs supply shocks is large (small). This over (under) weighting of the two objectives is only apparent , as it is in fact the logical consequence of having defind the mandate of the central bank in terms of one objective only.