The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
This appendix provides proofs of Theorems 1-3. Theorems 4-5 can be proved by following the same steps after conditioning on Z .
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.
