IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/23004.html
   My bibliography  Save this paper

On Future Allocations of Scarce Resources without Explicit Discounting Factors

Author

Abstract

In this paper, we show that by merely fixing upper bounds and lower bounds for the stream of consumptions, we can compute the optimal planning of consumptions independently from an explicit sequence of discounting factors as soon as they are assumed to be strictly decreasing. The optimal solution is unique and exhibits two regimes with a pivotal period in the middle. The same principle applies to future reimbursements of a debt as soon as we assume discounting factors to be strictly increasing. Therefore, one gets plans satisfying some kind of intergenerational fairness since: the highest effort is supported by the first generations and then it decreases for the remaining ones. Furthermore, we show that the solution is time consistent and we study the link with the standard discounted utilitarian model

Suggested Citation

  • Jean-Marc Bonnisseau & Alain Chateauneuf & Jean-Pierre Drugeon, 2023. "On Future Allocations of Scarce Resources without Explicit Discounting Factors," Documents de travail du Centre d'Economie de la Sorbonne 23004, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:23004
    as

    Download full text from publisher

    File URL: http://mse.univ-paris1.fr/pub/mse/CES2023/23004.pdf
    Download Restriction: no
    File URL: https://shs.hal.science/halshs-04013245
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fleurbaey, Marc & Zuber, Stéphane, 2015. "Discounting, risk and inequality: A general approach," Journal of Public Economics, Elsevier, vol. 128(C), pages 34-49.
    2. Fleurbaey, Marc & Zuber, Stéphane, 2015. "Discounting, beyond utilitarianism," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 9, pages 1-52.
    3. Kaushik Basu & Tapan Mitra, 2003. "Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian," Econometrica, Econometric Society, vol. 71(5), pages 1557-1563, September.
    4. Marc Fleurbaey & Stéphane Zuber, 2012. "Climate policies deserve a negative discount rate," Working Papers halshs-00728193, HAL.
    5. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    6. Marcello Basili & Alain Chateauneuf, 2020. "Aggregation of experts' opinions and conditional consensus opinion by the Steiner point," Post-Print hal-03260206, HAL.
    7. repec:hal:pseose:hal-01300594 is not listed on IDEAS
    8. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1449-1499.
    9. Christopher P. Chambers & Federico Echenique, 2018. "On Multiple Discount Rates," Econometrica, Econometric Society, vol. 86(4), pages 1325-1346, July.
    10. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. repec:hal:pseose:hal-01300618 is not listed on IDEAS
    12. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    13. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    14. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Pierre Drugeon & Thai Ha Huy, 2022. "A not so myopic axiomatization of discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 349-376, February.
    2. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Lorenzo Bastianello & Jos'e Heleno Faro, 2019. "Time discounting under uncertainty," Papers 1911.00370, arXiv.org, revised Mar 2020.
    4. Lorenzo Bastianello & José Heleno Faro, 2023. "Choquet expected discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May.
    5. Drugeon, Jean-Pierre & Ha-Huy, Thai, 2023. "An α-MaxMin utility representation for close and distant future preferences with temporal biases," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    6. Jean-Pierre Drugeon & Thai Ha-Huy, 2018. "Towards a Decomposition for the Future: Closeness, Remoteness & Temporal Biases," PSE Working Papers halshs-01962035, HAL.
    7. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    8. Jean-Pierre Drugeon & Thai Ha-Huy, 2023. "An $\alpha$-MaxMin Utility Representation for Close and Distant Future Preferences with Temporal Biases," PSE Working Papers hal-04010969, HAL.
    9. Jean-Pierre Drugeon & Thai Ha-Hui, 2023. "An a-MaxMin Utility Representation for Close and Distant Future Preferences with Temporal Biases," Documents de recherche 23-08, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    10. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    11. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    12. Nina Anchugina, 2017. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Theory and Decision, Springer, vol. 82(2), pages 185-210, February.
    13. Nina Anchugina, 2015. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Papers 1511.06454, arXiv.org.
    14. Drugeon, Jean-Pierre & Ha-Huy, Thai, 2021. "On Multiple Discount Rates with Recursive Time-Dependent Orders," MPRA Paper 111308, University Library of Munich, Germany.
    15. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(C).
    16. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    17. Stefan A. Lipman & Arthur E. Attema, 2024. "A systematic review of unique methods for measuring discount rates," Journal of Risk and Uncertainty, Springer, vol. 69(2), pages 145-189, October.
    18. Susumu Cato, 2020. "Quasi-stationary social welfare functions," Theory and Decision, Springer, vol. 89(1), pages 85-106, July.
    19. Philip Streich & Jack S. Levy, 2007. "Time Horizons, Discounting, and Intertemporal Choice," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(2), pages 199-226, April.
    20. Pier-André Bouchard St-Amant & Jean-Denis Garon, 2015. "Optimal redistributive pensions and the cost of self-control," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 22(5), pages 723-740, October.

    More about this item

    Keywords

    intertemporal allocation; multiple regimes; discount rates; fairness; probability intervals; capacities;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

    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:mse:cesdoc:23004. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.