Efficiency with endogenous population growth

In this paper, we generalize the notion of Pareto efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed: -efficiency and -efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto efficiency when fertility is exogenous. We prove a version of the first welfare theorem for Barro-Becker type fertility choice models and discuss how this result can be generalized. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and we classify them into settings where inefficiencies arise inside the family and settings where they arise across families.