This paper studies the patterns of trade and the incentives to innovate in an unequal global economy. We introduce non-homothetic preferences in a general-equilibrium model of endogenous growth and international trade between two countries, and argue that the effects of market integration on the consequent trade patterns and the incentives to innovate depend on the degree of income inequality across countries. We find that if inequality across countries is low, the extensive margin of trade between countries is high whereas the world growth rate is low. The introduction of non-homothetic preferences rises a number of interesting questions that are not an issue in the standard model. For example, we discuss the design of intellectual property rights, in particular national vs. international exhaustion of patents, and argue that households in poor and rich countries might not see eye to eye depending on how poor households weigh future losses in consumption against present gains. Furthermore, we address the welfare consequences of a trade liberalization, and show that households in the poor country might loose relative to households in the rich country if trade costs fall from a high to a sufficiently low level.