Optimal longevity of a dynasty

A standard roundabout production framework is considered in a dynastic social welfare maximization problem, incorporating critical-level utilitarianism as the guiding principle for social welfare. While critical-level utilitarianism has been established to studying the optimal population size in a static and equitable manner, we apply the same axiology in a dynamic context with respect to capital accumulation and savings and study the optimal generation size, possibly without discounting future generations. Our study is based on a finite-horizon dynamic programming technique. We apply this technique to obtain optimal consumption schedules under a given planning horizon. The findings suggest that the optimal planning horizon (i.e., the optimal generation size) is not necessarily infinite, even when future generations are treated under conditions of ultimate equity.