In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-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 then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. We discuss two sets of sufficient conditions for noncooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and classify them into ones where inefficiencies arise inside the family and ones where they arise across families.

Consumer bankruptcy provides partial insurance against bad luck, but, by driving up interest rates, makes life-cycle smoothing more difficult. We argue that to assess this trade-off one needs a quantitative model of consumer bankruptcy with three key features: life-cycle component, idiosyncratic earnings uncertainty, and expense uncertainty (exogenous negative shocks to household balance sheets). We find that transitory and persistent earnings shocks have very different implications for evaluating bankruptcy rules. More persistent shocks make the bankruptcy option more desirable. Larger transitory shocks have the opposite effect. Our findings suggest the current US bankruptcy system may be desirable for reasonable parameter values.