Efficiency and endogenous fertility

This paper explores the properties of the notions of A-efficiency and P-efficiency, which were proposed by Golosov et al. (2007), to evaluate allocations in a general overlapping generations setting in which fertility choices are endogenously selected from a continuum and any two agents of the same generation are identical. First, we show that the properties of A-efficient allocations vary depending on the criterion used to identify potential agents. If one identifies potential agents by their position in their siblings' birth order, as Golosov, Jones, and Ter-tilt do, then A-efficiency requires that a positive measure of agents use most of their endowment to maximize the utility of the dynasty head, which, in environments with finite-horizon altruism, implies that some agents-the youngest in every family-obtain an arbitrary low income to finance their own consumption and fertility plans. If potential agents are identified by the dates in which they may be born, then A-efficiency reduces to dynastic maximization, which, in environments with finite-horizon altruism, drives the economy to a collapse in finite time. To deal with situations like those arising in economies with finite-horizon altruism, in which A-efficiency may be in conflict with individual rights, we propose to evaluate the efficiency of a given allocation with a particular class of specifications of P-efficiency for which the utility attributed to the unborn depends on the utility obtained by their living siblings. Under certain concavity assumptions on value functions, we also characterize every symmetric, P-efficient allocation as a Millian efficient allocation, that is, as a symmetric allocation that is not A-dominated-with the birth-order criterion-by any other symmetric allocation.