We develop a theory of multiproduct firms to analyze the  effects of globalization on the distributions of firm size, scope, and productivity. Our model explains two puzzles. First, it explains the well-known size-discount puzzle: large firms have lower values of Tobin’s Q than small firms. Second, it explains the globalization-skewness puzzle documented in the empirical part of our paper: a multilateral reduction in trade costs leads to a flattening of the size distribution of firms. In our model, globalization not only affects the distribution of observed productivities but also productivity at the firm level.