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In a monetary union, inflation rate differentials may be substantial over the business cycle. This paper parameterizes a monetary union with cross-country structural differences in (i) the elasticity of demand in the goods markets, (ii) the degree of price inertia and (iii) the preference for foreign goods in consumption. The model, calibrated to reproduce two large EMU countries, is able to generate non-negligible inflation differentials in response to symmetric shocks. The mechanism of price discrimination is the most important one, but moderate differences in the degree of openness have sizeable effects on the dispersion of inflation rates if idiosyncratic shocks predominate.