A large literature considers the optimal size and growth rate of the human
population, trading off the utility value of additional people with the costs of a larger
population. In this literature, an important parameter is the social weight placed on
population size; a standard result is that a planner with a larger weight on population
chooses larger population levels and growth rates. We demonstrate that this result
is conditionally overturned when an exhaustible resource constraint is introduced:
if the discount rate is small enough, the optimal population today decreases with
the welfare weight on population size. That is, a more total-utilitarian social planner
could prefer a smaller population today than a more average-utilitarian social planner.
We also present a numerical illustration applied to the case of climate change, where
we show that under plausible real-world parameter values, our result matters for the
direction and magnitude of optimal population policy.

• Optimal population and exhaustible resource constraints