In recent decades, most industrialized countries experienced declining population growth rates caused by declining fertility and associated with rising life expectancy. We analyze the effect of continuing demographic change on medium- and long-run economic growth by setting forth an R&D-based growth model including an analytically tractable demographic structure. Our results show that, in response to demographic change, technological progress and economic growth accelerate in the medium run but slow down in the long run. Numerical investigation reveals that the time period during which technological progress and economic growth are faster than without demographic change can be very long. Since the theoretical predictions for the medium run are consistent with the negative association between population growth and economic growth found in the empirical literature, the present framework can reconcile R&D-based growth theory with the available empirical evidence.