It is widely recognized that the Euro area is an asymmetric monetary union which assembles countries with heterogeneous structures on financial, goods and labour markets stricken by asymmetric shocks. However, the main objective of the European Central Bank (ECB) is to preserve price stability for the euro area as a whole, and the ECB pays most of its attention to union-wide output and (principally) inflation, neglecting, at least on the level of principles, inflation and output divergences in union. In this paper, we wonder, at a theoretical level, about the social loss associated with such an objective based on aggregate magnitudes, and we search for solutions, namely an “optimal” contract for a common central bank. We show in particular that it is not necessarily a good thing that a common central bank worries about inflation divergences without being concerned about output divergences in union.