In a monetary union, inflation rate differentials may be substantial over the business cycle. This paper parameterizes a two-country monetary union in which different economic structures in the two countries generate temporary inflation differentials. Cross-country differences are introduced in (i) the elasticity of demand in the goods markets, which cause producers to discriminate prices, (ii) the degree price inertia and (iii) openness or preference for foreign goods in consumption. The model is calibrated to reproduce two average big EMU countries and it is able to generate sizeable inflation differentials. We find the mechanism of price discrimination quantitatively more important than the differences in price inertia. Moreover, under asymmetric shocks, differences in the degree of openness as the ones observed within the EMU can have sizeable effects on the dispersion of inflation rates.