This paper develops a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. The model captures the empirical observation that higher firm-level ability raises productivity across all products, leading to a positive correlation between a firm's intensive (output per product) and extensive (number of products) margins. Trade liberalization fosters productivity growth within and across firms by inducing firms to drop marginally productive products and force low-productivity firms to exit. Exporters, despite producing a smaller range of products, increase the share of products sold abroad and exports per product. These adjustments are more pronounced in countries' comparative advantage industries. The model highlights the role of endogenous product scope in shaping firm dynamics and provides a micro-foundation for the idea that international trade spurs firms to rationalize production. The paper also examines the impact of trade liberalization on firm entry and exit, and the distribution of firm size, emphasizing the positive correlation between firms' intensive and extensive margins.This paper develops a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. The model captures the empirical observation that higher firm-level ability raises productivity across all products, leading to a positive correlation between a firm's intensive (output per product) and extensive (number of products) margins. Trade liberalization fosters productivity growth within and across firms by inducing firms to drop marginally productive products and force low-productivity firms to exit. Exporters, despite producing a smaller range of products, increase the share of products sold abroad and exports per product. These adjustments are more pronounced in countries' comparative advantage industries. The model highlights the role of endogenous product scope in shaping firm dynamics and provides a micro-foundation for the idea that international trade spurs firms to rationalize production. The paper also examines the impact of trade liberalization on firm entry and exit, and the distribution of firm size, emphasizing the positive correlation between firms' intensive and extensive margins.