"We study international trade in a model where consumers have non-homothetic preferences and where household income restricts the extensive margin of consumption. In equilibrium, monopolistic producers set high (low) prices in rich (poor) countries but a threat of parallel trade restricts the scope of price discrimination between countries. The threat of parallel trade allows differences in per capita incomes to have a strong impact on the extensive margin of trade, whereas differences in population sizes have a weaker effect. We also show that the welfare gains from trade liberalization are biased towards rich countries. We extend our model to more than two countries; to unequal incomes within countries; and to more general specifications of non-homothetic preferences. Our basic results are robust to these extensions."