This paper presents a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. The model incorporates firm-level "ability" and firm-product-level "expertise" as stochastic and unknown prior to entry. Higher firm ability increases productivity across all products, leading to a positive correlation between firms' intensive (output per product) and extensive (number of products) margins. Trade liberalization fosters productivity growth within and across firms by inducing firms to shed marginally productive products and forcing the lowest-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 introduces endogenous product scope, allowing firms to adjust their range of products in response to trade liberalization. This creates a new margin of firm adjustment, generating novel firm and industry dynamics. The model shows that trade liberalization leads to a positive correlation between firms' intensive and extensive margins, magnifying inequality in the firm-size distribution and having general equilibrium implications for entry and exit. The model also highlights that trade liberalization pressures firms to focus on their "core competencies," leading to endogenous Ricardian productivity differences and magnifying Heckscher-Ohlin-based comparative advantage. The model is supported by empirical evidence showing that multi-product firms dominate U.S. manufacturing and trade, with substantial heterogeneity in products within firms. The model's predictions are consistent with empirical findings, including the positive correlation between firms' intensive and extensive margins and the role of international trade in shaping firm and industry productivity. The model also shows that trade liberalization leads to increased productivity growth within and across firms, with the strongest effects in countries' comparative advantage industries. The model provides an intuitive micro-foundation for the idea that international trade spurs firms to rationalize production, without implying money being left on the table prior to liberalization.This paper presents a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. The model incorporates firm-level "ability" and firm-product-level "expertise" as stochastic and unknown prior to entry. Higher firm ability increases productivity across all products, leading to a positive correlation between firms' intensive (output per product) and extensive (number of products) margins. Trade liberalization fosters productivity growth within and across firms by inducing firms to shed marginally productive products and forcing the lowest-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 introduces endogenous product scope, allowing firms to adjust their range of products in response to trade liberalization. This creates a new margin of firm adjustment, generating novel firm and industry dynamics. The model shows that trade liberalization leads to a positive correlation between firms' intensive and extensive margins, magnifying inequality in the firm-size distribution and having general equilibrium implications for entry and exit. The model also highlights that trade liberalization pressures firms to focus on their "core competencies," leading to endogenous Ricardian productivity differences and magnifying Heckscher-Ohlin-based comparative advantage. The model is supported by empirical evidence showing that multi-product firms dominate U.S. manufacturing and trade, with substantial heterogeneity in products within firms. The model's predictions are consistent with empirical findings, including the positive correlation between firms' intensive and extensive margins and the role of international trade in shaping firm and industry productivity. The model also shows that trade liberalization leads to increased productivity growth within and across firms, with the strongest effects in countries' comparative advantage industries. The model provides an intuitive micro-foundation for the idea that international trade spurs firms to rationalize production, without implying money being left on the table prior to liberalization.