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We study patterns of foreign direct investment (FDI) in a multi-country world economy. We develop a model featuring non-homothetic preferences for quality and monopolistic competition in which specialization is purely demand-driven and the decision to serve foreign countries via exports or FDI depends on a proximity-concentration trade-off. We characterize the joint patterns of trade and FDI when countries differ in income distribution and size and show that FDI is more likely to occur between countries with similar per capita income levels. The model predicts a Linder Hypothesis for horizontal FDI, which is consistent with some patterns we find using establishment-level data on multinational activity.