We build a two-country DSGE model for a currency union, with habit formation, product and labour differentiation and nominal rigidities, and monetary policy follows an ad-hoc rule. The main innovation is the incorporation of several sources of heterogeneity and the assessment of its impact on welfare. From the formal utility-based welfare analysis, we find that nominal rigidities are the most important source of heterogeneity. In a currency union where the central bank responds area wide and does not take into account national differences, it would be desirable to lower the overall level of rigidity in both countries at the same time, as there are significant welfare losses when country heterogeneity rises. A comparison of different policy rules allows us to conclude that rules that weigh more inflation relatively to the output gap provide the best result in terms of welfare. We also find out that if the central bank can take into account differences in nominal rigidities levels between countries, then it is preferable to react more strongly to the more rigid country.