Between 1950 and 2017, world average life expectancy increased from below-50 to above-70, while the fertility rate dropped from 5 to about 2.5. We develop and calibrate an analytic climate-economy model with overlapping generations to study the effect of such demographic change on capital markets and optimal climate policies. Our model replicates findings from the OLG-demography literature, such as a rise in households’ savings, and a declining rate of return to capital. We also find that demographic change raises the social cost of carbon, at 2020, from 28 euro/tCO2 in a model that abstracts from demography, to 94 euro/tCO2 in our calibrated model.