A cap on greenhouse gas emissions makes total emissions a fixed common-property resource. Population increases under a cap are therefore self-limiting: a population increase raises labor and reduces emissions per unit of labor, which lowers incomes and fertility. Because a marginal birth under a cap lowers all incomes, a cap induces a negative population externality. The externality is substantial in calibrations, about 20 percent of income in steady state and 5 percent of income immediately after imposition, or more, per child. Similarly, the optimal population may be one-quarter of the natural population in steady state.
population externality Pigovian tax emissions cap endogenous fertility economic growth optimal population calibrated optimal child tax