This paper analyzes optimal monetary and fiscal policy in a monetary union from a union-wide perspective, using a multi-country New Keynesian business-cycle model with rigid real wages. Fiscal policy is implemented at the country level through decisions regarding government spending, while the monetary authority sets a common nominal interest rate. It is found that in the presence of country-specific shocks as well as symmetric shocks, there is a country-level trade-off between stabilizing inflation and the output gap. After a union-wide shock, the common monetary authority also faces a trade-off. If shocks are symmetric, the optimal union-wide policy requires that the common central bank conduct a countercyclical policy, allowing for more relative inflation volatility than the amount actually allowed by the ECB. The role of policies is reversed at the domestic level, where the government stabilizes the economy via a countercyclical policy, regardless of whether shocks are symmetric.