Millian Efficiency with Endogenous Fertility

This paper is concerned with an extension of the notion of Pareto efficiency, referred to as Millian efficiency, to evaluate the performance of symmetric allocations in an overlapping generations setting with endogenous fertility. The criterium of Pareto dominance underlying the notion of Millian efficiency is based exclusively on preferences of those agents who are actually born, and allows only for welfare comparisons of symmetric allocations (i.e, allocations in which all living individuals of the same generation take the same decisions). The main contributions of the paper are the following. First, we provide necessary (static) and sufficient (dynamic) conditions to determine whether an allocation is Millian efficient or not, and we show that the sufficient conditions for dynamic efficiency offered by Cass (1972) and Balasko and Shell (1980) cannot be straightforward applied when fertility decisions are endogenous. Second, we extend the two Fundamental Theorems of Welfare Economics to a framework with endogenous population by characterizing Millian efficient allocations as the equilibria of a decentralized price mechanism. Finally, we present a condition to identify equilibrium allocations as dynamically efficient that exclusively uses the sequence of prices associated to such decentralized equilibria.