The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: Jul, 2007, Volume 75, Issue 4
https://doi.org/10.1111/j.1468-0262.2007.00781.x
p. 1039-1071
Mikhail Golosov, Larry E. Jones, Michèle Tertilt
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 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 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.
In this Appendix we provide additional details on some of the ideas developed in the paper, "Efficiency with Endogenous Population Growth," (2006). We first give the formal proof that A-efficiency is generically non-empty. The second section extends the notions of efficient fertility developed in the paper for the discrete case to environments in which fertility is a continuous choice variable. It also provides an extension of the First Welfare Theorem, given in the paper for the discrete case, to the continuous case. The second section gives an explicit example of an economy with negative externalities. We show that a negative externality can lead to too many people in equilibrium in the A-sense, and also show how to decentralize A-efficient allocations through Pigouvian tax systems. The third section provides a proof that the limit of the equilibria of the finite horizon B&B games exists, and is an equilibrium of the infinite horizon B&B game.
In this Appendix we provide additional details on some of the ideas developed in the paper, "Efficiency with Endogenous Population Growth," (2006). We first give the formal proof that A-efficiency is generically non-empty. The second section extends the notions of efficient fertility developed in the paper for the discrete case to environments in which fertility is a continuous choice variable. It also provides an extension of the First Welfare Theorem, given in the paper for the discrete case, to the continuous case. The second section gives an explicit example of an economy with negative externalities. We show that a negative externality can lead to too many people in equilibrium in the A-sense, and also show how to decentralize A-efficient allocations through Pigouvian tax systems. The third section provides a proof that the limit of the equilibria of the finite horizon B&B games exists, and is an equilibrium of the infinite horizon B&B game.
