Optimal Population in a Finite Horizon

TL;DR

This paper develops a dynamic model to determine optimal population schedules over a finite horizon, balancing social welfare and resource constraints through technological innovation and energy depletion considerations.

Contribution

It introduces a novel finite-horizon optimization framework incorporating resource depletion and technological progress to determine optimal population policies.

Findings

Trade-offs between utilitarian and maximin welfare criteria are visualized.

Technological innovations can postpone resource depletion.

Optimal population schedules depend on resource and welfare considerations.

Abstract

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.