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We develop a general equilibrium monopolistic competition model of trade with technical heterogeneity among firms and countries. With free entry, technical asymmetries between firms result in the endogenous determination of the equilibrium average efficiency of the industry. We show that trade reduces (increases) the minimum efficiency required to survive in the more (less) efficient country. This has important welfare implications: (1) Contrary to the constant elasticity of substitution homogeneous-firms model, trade affects welfare even when there is no love of variety. (2) There are circumstances in which trade liberalization leads to a loss of consumer welfare.