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The MBR intertemporal choice criterion and Rawls’ just savings principle

Author

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  • Charles Figuières

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Ngo Van Long

    (Department of Economics [Montréal] - McGill University = Université McGill [Montréal, Canada])

  • Mabel Tidball

    () (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

Abstract

This paper provides general theorems about the control that maximizes the mixed Bentham–Rawls (MBR) criterion for intergenerational justice, which was introduced in Alvarez-Cuadrado and Long (2009). We establish sufficient concavity conditions for a candidate trajectory to be optimal and unique. We show that the state variable is monotonic under rather weak conditions. We also prove that inequality among generations, captured by the gap between the poorest and the richest generations, is lower when optimization is performed under the MBR criterion rather than under the discounted utilitarian criterion. A quadratic example is also used to perform comparative static exercises: it turns out, in particular, that the larger the weight attributed to the maximin part of the MBR criterion, the better-off the less fortunate generations. All those properties are discussed and compared with those of the discounted utilitarian (DU, Koopmans 1960) and the rank-discounted utilitarian (RDU, Zuber and Asheim, 2012) criteria. We contend they are in line with some aspects of the rawlsian just savings principle.

Suggested Citation

  • Charles Figuières & Ngo Van Long & Mabel Tidball, 2017. "The MBR intertemporal choice criterion and Rawls’ just savings principle," Post-Print hal-01505772, HAL.
  • Handle: RePEc:hal:journl:hal-01505772
    DOI: 10.1016/j.mathsocsci.2016.10.009
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01505772
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    References listed on IDEAS

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    1. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2009. "A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 154-168, September.
    2. Geir B. Asheim, 2010. "Intergenerational Equity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 197-222, September.
    3. Charles Figuières & Mabel Tidball, 2016. "Sustainable Exploitation of a Natural Resource: A Satisfying Use of Chichilnisky’s Criterion," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 207-229, Springer.
    4. Geir B. Asheim, 1988. "Rawlsian Intergenerational Justice as a Markov-Perfect Equilibrium in a Resource Technology," Review of Economic Studies, Oxford University Press, vol. 55(3), pages 469-483.
    5. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
    6. Tol, Richard S.J., 2013. "Climate policy with Bentham–Rawls preferences," Economics Letters, Elsevier, vol. 118(3), pages 424-428.
    7. Estelle Midler & Charles Figuières & Marc Willinger, 2015. "Choice overload, coordination and inequality: three hurdles to the effectiveness of the compensation mechanism?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 513-535, October.
    8. Long, Ngo Van, 1979. "Two Theorems on Generalized Diminishing Returns and Their Applications to Economic Analysis," The Economic Record, The Economic Society of Australia, vol. 55(148), pages 58-63, March.
    9. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    10. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
    11. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    12. John Roemer, 2011. "The Ethics of Intertemporal Distribution in a Warming Planet," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(3), pages 363-390, March.
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    Cited by:

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    2. Walter Bossert & Kohei Kamaga, 2020. "An axiomatization of the mixed utilitarian–maximin social welfare orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 451-473, March.
    3. Hartwick, John M. & Long, Ngo Van, 2018. "Sustainability with endogenous discounting when utility depends on consumption and amenities," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 31-36.

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