Efficiency and Endogenous Fertility

Abstract

This paper explores the properties of several notions of efficiency (A..efficiency, P..efficiency and Millian efficiency) to evaluate allocations in a general overlapping generations setting with endogenous fertility and descendant altruism that includes, as a particular case, Barro and Becker's (1988) model of fertility choice. We rst focus on the notion of A..efficiency, proposed by Golosov, Jones and Tertilt (Econometrica, 2007) and show that, in many environments, the set of symmetric, interior, A..efficient allocations is empty. To overcome this problem, we then propose to evaluate the efficiency of a given allocation with a particular specication of P..efficiency {proposed also by Golosov et al.{ for which the utility attributed to the unborn depends on the utility level achieved by those who get to be born in a given allocation. For a large class of specications of the function determining the utility attributed to the unborn, every Millian efficient allocation, that is, every symmetric allocation that is not A..dominated by any other symmetric allocation, is also P-efficient. Finally, we restate the First Welfare Theorem by showing that a) every competitive equilibrium is a {statically{ Millian efficient allocation; and that b) if long-run wages do not exceed the capitalized costs of rearing children, then competitive equilibria are also {dynamically{ Millian efficient.