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On the (Ir)Relevance of Discount Factors for Future Allocations of Scarce Resources

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  • Jean-Marc Bonnisseau

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Alain Chateauneuf

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Jean-Pierre Drugeon

    (CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This article is interested in future allocations of scarce resources in an environment where upper bounds and lower bounds are fixed on the stream of consumptions or extractions of the scarce resource. It is shown that we can compute the optimal planning of consumptions independently from an explicit sequence of discounting factors as soon as they are decreasing at a rate smaller than a bound linked to the concavity of the utility function and the choice of the sequences of lower and upper bounds. The optimal solution is unique and exhibits two regimes with a pivotal period in the middle. Therefore, one gets plans satisfying some kind of intergenerational fairness: while the highest e ort is supported by the first generations, it then decreases for the remaining ones. The argument is then extended to partially renewable resources. Finally, we consider the role of the horizon and of a potential regret after a revision for the bounds.

Suggested Citation

  • Jean-Marc Bonnisseau & Alain Chateauneuf & Jean-Pierre Drugeon, 2025. "On the (Ir)Relevance of Discount Factors for Future Allocations of Scarce Resources," Working Papers halshs-04916616, HAL.
    • Handle: RePEc:hal:wpaper:halshs-04916616
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04916616v1
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