IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.15978.html
   My bibliography  Save this paper

Optimal longevity of a dynasty

Author

Listed:
  • Satoshi Nakano
  • Kazuhiko Nishimura

Abstract

The welfare of a dynasty that consists of identical Bernoullian utilities subject to Cobb-Douglas production with constant labor is maximized. We blend two discounting schemes to avoid the objective function from exploding to infinity: one is the compound discounting of future utilities and the other is the binary discounting which undiscounts utilities before the planning horizon but fully discounts those that lie beyond. After presenting a general solution to the optimal schedule of consumption, we study the planning solution analytically and also numerically, to discover that the optimal planning horizon is not necessarily an infinity, even under the case of zero compound discounting. Furthermore, we study the inequality of consumptions among generations with respect to the compound discount rates and planning horizons.

Suggested Citation

  • Satoshi Nakano & Kazuhiko Nishimura, 2024. "Optimal longevity of a dynasty," Papers 2409.15978, arXiv.org.
    • Handle: RePEc:arx:papers:2409.15978
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.15978
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2409.15978. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.