Optimal longevity of a dynasty
Abstract
Standard optimal growth models implicitly impose a ``perpetual existence'' constraint, which can ethically justify infinite misery in stagnant economies. This paper investigates the optimal longevity of a dynasty within a Critical-Level Utilitarian (CLU) framework. By treating the planning horizon as an endogenous choice variable, we establish a structural isomorphism between static population ethics and dynamic growth theory. Our analysis derives closed-form solutions for optimal consumption and longevity in a roundabout production economy. We show that under low productivity, a finite horizon is structurally optimal to avoid the creation of lives not worth living. This result suggests that the termination of a dynasty can be interpreted not as a failure of sustainability, but as an {altruistic termination} to prevent intergenerational suffering. We also highlight an ethical asymmetry: while a finite horizon is optimal for declining economies, growing economies under intergenerational equity demand the ultimate sacrifice from the current generation.
Keywords
Cite
@article{arxiv.2409.15978,
title = {Optimal longevity of a dynasty},
author = {Satoshi Nakano and Kazuhiko Nishimura},
journal= {arXiv preprint arXiv:2409.15978},
year = {2026}
}