Optimal longevity of a dynasty

[2409.15978] Optimal longevity of a dynasty Skip to main content Search Submit Donate Log in Economics > General Economics arXiv:2409.15978 (econ) [Submitted on 24 Sep 2024 ( v1 ), last revised 21 Aug 2026 (this version, v7)] Title: Optimal longevity of a dynasty Authors: Satoshi Nakano , Kazuhiko Nishimura View PDF HTML (experimental) 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. Subjects: General Economics (econ.GN) Cite as: arXiv:2409.15978 [econ.GN] (or arXiv:2409.15978v7 [econ.GN] for this version) https://doi.org/10.48550/arXiv.2409.15978 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Homo Oeconomicus (2026) Related DOI : https://doi.org/10.1007/s41412-026-00162-7 Focus to learn more DOI(s) linking to related resources Submission history From: Kazuhiko Nishimura [ view email ] [v1] Tue, 24 Sep 2024 11:20:26 UTC (106 KB) [v2] Sun, 29 Dec 2024 17:26:15 UTC (317 KB) [v3] Sun, 6 Jul 2025 03:12:04 UTC (318 KB) [v4] Wed, 31 Dec 2025 09:10:16 UTC (325 KB) [v5] Sat, 21 Feb 2026 05:14:02 UTC (326 KB) [v6] Fri, 5 Jun 2026 13:28:52 UTC (330 KB) [v7] Fri, 21 Aug 2026 19:24:26 UTC (330 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: econ.GN < prev | next > new | recent | 2024-09 Change to browse by: econ q-fin q-fin.EC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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