Optimal longevity of a dynasty

TL;DR

This paper explores the ethical and economic implications of determining the optimal lifespan of a dynasty using a critical-level utilitarian framework, revealing conditions for finite or infinite longevity based on productivity and growth.

Contribution

It introduces a novel endogenous planning horizon in growth models, linking population ethics with dynamic economic theory, and provides closed-form solutions for optimal longevity and consumption.

Findings

Finite horizon is optimal under low productivity to prevent suffering.

Infinite longevity can be justified in growing economies with intergenerational equity.

Ethical asymmetry exists between declining and growing economies regarding dynasty length.

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.