Malthusian stagnation is efficient

This article studies socially optimal allocations, from the point of view of a benevolent social planner, in environments characterized by fixed resources, endogenous fertility, and full information. Individuals in our environment are fully rational and altruistic toward their descendants. Our model allows for rich heterogeneity of abilities, preferences for children, and costs of raising children. We show that the planner's optimal allocations are efficient in the sense of Golosov et al. (2007). We also show that efficient allocations in the endogenous fertility case differ significantly from its exogenous fertility counterpart. In particular, optimal steady-state population is proportional to the amount of fixed resources and the level of technology while steady-state individual consumption is independent of these variables, a sort of a "Malthusian stagnation" result. Furthermore, optimal allocations exhibit inequality, differential fertility, random consumption, and a higher population density of poorer individuals even when the planner is fully equalitarian, and faces no aggregate risk nor frictions.