We study the North-South diffusion of technologies embodied in internationally mobile capital in a framework of intertemporal global welfare maximization. Convergence of the growth rates of technical change in the North and South always occurs in the long-run. However, the degree to which the North-South technology gap can be narrowed depends crucially on the level of the absorptive capacity (human capital, infrastructure, legal framework, etc.) in the South. Performing own innovations in the South narrows the technology gap only in the short-run. An optimal development policy requires more capital to be allocated to the South in earlier stages of development. Allowing for optimal investment into the absorptive capacity, the absorptive capacity rises steadily with the aim to close the technology gap completely. Our results show that an optimal development policy requires FDI to be matched by investment into the absorptive capacity.