This project investigates the consequences of demographic change on economic growth when technological change is endogenously driven by R&D. Qualitatively, population ageing generates two opposing transitional forces: increased R&D and capital investments on the one hand, and an increasing old-age dependency ratio on the other. I evaluate these channels quantitatively along the demographic transition using a calibrated overlapping generations model with idiosyncratic, uninsurable productivity shocks, mortality risk, intensive and extensive margins of labour supply and endogenous technological change. Considering the United States, I find that demographic change improved growth throughout the latter half of the twentieth century. Consistent with the empirical observation of recently declining growth rates, ageing also accounts for a 0.5 percentage point drop in growth since 2000 and is predicted to keep growth rates low throughout the twenty-first century. Decomposing the growth rate reveals that technological change is an important driver of these results, accounting for 50 percent of cumulative growth between 1950 and 2100.