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We explore the effect of trade policy on productivity and welfare in the now standard model of firm-level heterogeneity and product differentiation with monopolistic competition. To obtain sharp results, we restrict attention to an economy that takes as given the price of imports and the demand schedules for its exports (a "small economy"). We first establish that welfare can be decomposed into four terms: productivity, terms of trade, variety and curvature, where the last is a term that captures heterogeneity across varieties. We then show how a consumption subsidy, an export tax, or an import tariff allows our small economy to deal with two distortions that we identify and thereby reach its first-best allocation. We also show that an export subsidy generates an increase in productivity, but given the negative joint effect on the other three terms (terms of trade, variety, and curvature), welfare falls. In contrast, an import tariff improves welfare in spite of the fact that productivity falls.