In this paper we present an optimizing-agent model for the euro area to emphasize how the existence of heterogencity in inflation persistence across regions matter for the design of monetary policy. We find supporting evidence of the existence of such a heterogencity in inflation dynamics across euro area countries. In particular, based on the estimation of New Keynesian Phillips Curves for five major countries of the euro area, we find that inflation in Germany has a dominant forward-looking component, while in the other groups of countries inflation show a significant inertial (backwards looking) behaviour. Under this circumstance, we study the welfare implication of four monetary policy rules following terms-of-trade shocks: fully optimal, optimal inflation targeting, HICP targeting, and output gap stabilization.