We analyze the short and long-run effects of demographic ageing - increased longevity and reduced fertility - on per-capita growth. The OLG model captures direct effects, working through adjustments in the savings rate, labor supply, and capital deepening, and indirect effects, working through changes of taxes, government spending components and the retirement age in politico-economic equilibrium. Growth is driven by capital accumulation and productivity increases fueled by public investment. The closed-form solutions of the model predict taxation and the retirement age in OECD economies to increase in response to demographic ageing and per-capita growth to accelerate. If the retirement age was held constant, the growth rate in politico-economic equilibrium would essentially remain unchanged, due to a surge of social-security transfers and crowding out of public investment.