The paper employs an extended Yaari-Blanchard model of overlapping generations to study how the macroeconomy is affected over time by various demographic changes. It is shown that a proportional decline in fertility and death rates has qualitatively similar effects to capital income subsidies; both per capita savings and per capita consumption increase in the new steady state. A drop in the birth rate, although keeping the death rate constant, reduces per capita savings, but increases per capita consumption if the generational turnover effect is dominated by the intertemporal labor supply effect. If the generational turnover effect is sufficiently strong, however, a decline in the birth rate may, contrary to standard results, give rise to an increase in per capita savings. Finally, a fertility rate reduction that leaves unaffected the rate of generational turnover is shown to have effects qualitatively similar to those of a fall in public consumption. Both per capita savings and per capita output decline, but per capita private consumption rises.