Optimal Population in a Finite Horizon

A favorable population schedule for the entire potential human family is sought, under the overlapping generations framework, by treating population (or fertility) as a planning variable in a dynamical social welfare maximization context. The utilitarian and maximin social welfare functions are examined, with zero future discounting, while infinity in the maximand is circumvented by introducing the depletion of energy resources and its postponement through technological innovations. The model is formulated as a free-horizon dynamical planning problem, solved via a non-linear optimizer. Under exploratory scenarios, we visualize the potential trade-offs between the two welfare criteria.