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arXiv · 2409.15978

Optimal longevity of a dynasty

Satoshi Nakano·Kazuhiko Nishimura
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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.

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Satoshi Nakano, Kazuhiko Nishimura. 2024-09-24. Optimal longevity of a dynasty. https://arxiv.org/abs/2409.15978

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