The decline in the sensitivity of inflation to domestic slack observed in developed countries since the mid 1980’s has been often attributed to globalization. However, this intuition has so far not been formalized. I develop a general equilibrium setup in which the sensitivity of inflation to marginal cost decreases when international trade costs fall. In order to do so, I add three ingredients to an otherwise standard two-country new-Keynesian model. Strategic interactions generate a time varying desired markup; endogenous entry and heterogeneous productivity engender a self-selection of the most productive firms (also the largest ones) in international trade. Hence the weight of large firms in domestic production increases. These firms transmit less marginal cost fluctuations to price adjustments, rather absorbing them into their desired markup in order to protect their market share. At the aggregate level, domestic inflation reacts less to real activity fluctuations.