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We study a variation of the Eaton-Kortum model, a competitive, constant-returns-to-scale multicountry Ricardian model of trade. We establish existence and uniqueness of an equilibrium with balanced trade where each country imposes an import tariff. We analyze the determinants of the cross-country distribution of trade volumes, such as size, tariffs and distance, and compare a calibrated version of the model with data for the largest 60 economies. We use the calibrated model to estimate the gains of a world-wide trade elimination of tariffs, using the theory to explain the magnitude of the gains as well as the differential effect arising from cross-country differences in pre-liberalization of tariffs levels and country size.