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On Future Allocations of Scarce Resources without Explicit Discounting Factors

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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
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    File URL: http://mse.univ-paris1.fr/pub/mse/CES2023/23004.pdf
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    File URL: https://shs.hal.science/halshs-04013245
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    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

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