Abstract: The purpose of this paper is to analyze the dynamics of income distribution among countries integrated by trade. We derive a convergence equation for an integrated world, both in a neoclassical model and in an endogenous growth model. The convergence equation for an integrated world is similar to the well-known autarkic version, but has important differences: a) the growth rates of individual economies are positively affected by the growth rate of the world; (b) the rate of convergence increases as the world grows faster, and (c) the rate of convergence, under conventional parameter values, is far lower in an integrated world than in a world of autarkic economies. Thus the integrated world model can explain low rates of convergence frequently observed in empirical studies without imposing counterfactual parameter values or ad hoc restrictions on international borrowing and investment technologies.