Is Menopause Optimal?

Various theories have been put forward to explain the fact that humans experience menopause while virtually no animals do. This paper aims to investigate one such theory: children provide a savings technology into old age, but as human babies are usually large and have long gestation periods, a substantial risk of death exists for the mother as she bears children. It seems therefore appropriate to impose a stopping rule for fertility. Given an objective (support for old age) and demographics (mortality of mother and children), an optimal age for menopause can be calculated. Using demographic data from populations that have seen little influence from modern medicine, this optimal age is compared to empirical evidence.

Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.