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, P-efficiency and A-efficiency. The two concepts differ in how they treat people who are not born. We show how these concepts relate 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. Finally, we give two sets of sufficient conditions for non-cooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case"--National Bureau of Economic Research web site.