In spite of the structural heterogeneity of the Eurozone, the main objective of the European Central Bank (ECB) is to preserve price stability for the union as a whole, and she pays full attention to Union-wide inflation and output, neglecting national divergences. In this paper, we wonder, at a theoretical level, about the social loss associated with such a "centralized" objective, and we show the existence of an "optimal" contract for the common central bank, which ensures a correct stabilization of national magnitudes. Furthermore, we show that social welfare does not necessarily improve if the ECB worries about inflation divergences without being concerned about output divergences in the Union.

JEL Classification: E52, E58, F33