Efficiency and endogenous fertility
研究了在生育率内生选择的代际交叠模型中，两种效率概念（A效率和P效率）的性质，发现A效率可能导致家庭中最年轻成员收入极低或经济崩溃，并提出P效率作为替代方案。
This paper explores the properties of the notions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐efficiency and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">P</mi> </math>‐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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐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 Tertilt do, then <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">P</mi> </math>‐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, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">P</mi> </math>‐efficient allocation as a Millian efficient allocation, that is, as a symmetric allocation that is not <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi mathvariant="script">A</mi> </math>‐dominated—with the birth‐order criterion—by any other symmetric allocation.