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We study unilateral trade liberalization in a model of monopolistic competition with heterogeneous firms, endogenous wages, and non-separable and non-homothetic quadratic preferences that generate variable markups. We show that the optimal level of the revenue-generating import tariff is strictly positive so that protection is always desirable, whether the liberalizing economy is large or small. Yet, reductions in cost-shifting trade barriers are welfare-improving, making free trade optimal. Finally, we show that in both cases, variable markups result in negative pro-competitive effects, reducing gains from trade.