This paper argues that the per-capita income of importers is an important determinant of the extensive margin of trade. I formalize this by incorporating preferences that allow for binding nonnegativity constraints into an otherwise standard Ricardian model. This implies that agents adjust the set of goods from which they consume with income, which in turn affects the extensive margin of bilateral trade. I quantify the model using data on US consumer behavior and aggregate values of bilateral trade flows. I find that the behavior of the model’s extensive margin of bilateral trade is consistent with elasticities measured in the data. Two counterfactual experiments demonstrate the quantitative importance of the mechanism outlined in this paper.