This paper examines the impact of trade barriers on international trade flows by introducing firm heterogeneity into a model of international trade. In the Krugman (1980) model with identical firms, a higher elasticity of substitution between goods magnifies the impact of trade barriers on trade flows. However, when firm heterogeneity is introduced, particularly with a Pareto distribution of productivity, the predictions of the Krugman model are overturned. The impact of trade barriers on trade flows is dampened by the elasticity of substitution, not magnified. The paper introduces two margins of adjustment: the intensive margin, which refers to changes in the size of exports by existing firms, and the extensive margin, which refers to the entry of new firms into the export market. The elasticity of substitution has opposite effects on these margins. A higher elasticity of substitution makes the intensive margin more sensitive to changes in trade barriers, while it makes the extensive margin less sensitive. However, the dampening effect on the extensive margin dominates the magnifying effect on the intensive margin. The paper shows that when the distribution of productivity across firms is Pareto, which is close to the observed size distribution of US firms, the effect on the extensive margin dominates. The model predicts that total exports from country A to country B are given by an expression that includes an exponent inversely related to the elasticity of substitution. The elasticity of aggregate trade with respect to trade barriers is negatively related to the elasticity of substitution. The paper also discusses the implications of firm heterogeneity for trade flows. It shows that the presence of fixed costs and the extensive margin of trade is important for explaining trade flows. The model predicts that the elasticity of trade flows with respect to variable trade barriers, such as tariffs, is twice as large as it would be in the absence of firm heterogeneity. The paper also discusses the broader implications of the model for international trade theory. It shows that the presence of firm heterogeneity and the extensive margin of trade is important for explaining trade flows. The model provides a more accurate description of trade flows than traditional models, and it highlights the importance of the extensive margin in explaining trade flows. The paper concludes that the model with heterogeneous firms provides a more accurate description of trade flows than the Krugman model with identical firms.This paper examines the impact of trade barriers on international trade flows by introducing firm heterogeneity into a model of international trade. In the Krugman (1980) model with identical firms, a higher elasticity of substitution between goods magnifies the impact of trade barriers on trade flows. However, when firm heterogeneity is introduced, particularly with a Pareto distribution of productivity, the predictions of the Krugman model are overturned. The impact of trade barriers on trade flows is dampened by the elasticity of substitution, not magnified. The paper introduces two margins of adjustment: the intensive margin, which refers to changes in the size of exports by existing firms, and the extensive margin, which refers to the entry of new firms into the export market. The elasticity of substitution has opposite effects on these margins. A higher elasticity of substitution makes the intensive margin more sensitive to changes in trade barriers, while it makes the extensive margin less sensitive. However, the dampening effect on the extensive margin dominates the magnifying effect on the intensive margin. The paper shows that when the distribution of productivity across firms is Pareto, which is close to the observed size distribution of US firms, the effect on the extensive margin dominates. The model predicts that total exports from country A to country B are given by an expression that includes an exponent inversely related to the elasticity of substitution. The elasticity of aggregate trade with respect to trade barriers is negatively related to the elasticity of substitution. The paper also discusses the implications of firm heterogeneity for trade flows. It shows that the presence of fixed costs and the extensive margin of trade is important for explaining trade flows. The model predicts that the elasticity of trade flows with respect to variable trade barriers, such as tariffs, is twice as large as it would be in the absence of firm heterogeneity. The paper also discusses the broader implications of the model for international trade theory. It shows that the presence of firm heterogeneity and the extensive margin of trade is important for explaining trade flows. The model provides a more accurate description of trade flows than traditional models, and it highlights the importance of the extensive margin in explaining trade flows. The paper concludes that the model with heterogeneous firms provides a more accurate description of trade flows than the Krugman model with identical firms.