The dispersion of mark-ups in an open economy

We introduce heterogeneous mark-ups through Bertrand competition in a two-country model with endogenous firms' entry and tradability `a la Ghironi and Melitz (2005). Bertrand competition generates a distribution of mark-ups according to which firms that are larger and more productive charge lower prices, attract larger market shares and extract larger mark-ups. First, we characterize first-best allocations and their implementation. We find that they are inde- pendent from the degree of mark-ups' heterogeneity, suppress the dispersion of mark-ups and imply zero distortions on labor as well as substantial subsidies to preserve firm's incentives to enter. Second, second-best alternative policies with a restricted number of instruments and a balanced budget significantly reduce the potential welfare gains from fiscal policies. Third, the total welfare losses from passive policies are lower under heterogeneous mark-ups than under homogeneous mark-ups: while the dispersion of mark-ups has negative effects on the intensive margin, output per firm, it also raises expected profits for potential entrants and raises the ex- tensive margin, the number of firms in both domestic and export markets, pushing them closer to their efficient levels. Fourth, we also investigate the dynamic properties of allocations under passive and optimal policies considering aggregate productivity shocks and trade liberalization experiments.