We consider the interaction between the monetary policy of a common central bank in a monetary union, and the separate fiscal policies of the member countries. We construct a model of the Barro-Gordon type extended to many countries and countercyclical fiscal stabilization policies. Each country's fiscal policies inflict positive (output expansion) and negative (inflation) externalities on other countries, and the common monetary policy has its time-consistency problem. But we find that each kind of policy helps solve the other kind's problem. The first-best can be achieved despite the inevitability of some ex post monetary accommodation to fiscal profligacy, without the need for fiscal coordination, without the need for monetary commitment, without the need for a conservative central bank, and irrespective of whether the fiscal or the monetary authorities have the first move.