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Egalitarianism under population change: Age structure does matter

Author

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  • Boucekkine, R.
  • Fabbri, G.
  • Gozzi, F.
Abstract
We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarianism meant as “equal consumption for all individuals of all generations”. Social welfare functions are parameterized by an altruism parameter generating the Benthamite and Millian criteria as polar cases. The economy considered is in continuous time and is populated by homogeneous cohorts with a given life span. Production functions are linear in labor, (costly) procreation is the unique way to transfer resources forward in time. First, we show that egalitarianism is optimal whatever the degree of altruism in “perpetual youth” model, that is when lifetime span is finite but age structure does not matter: in this case egalitarianism does not discriminate between the social welfare functions considered. Then we show that, when life span is finite but age structure matters, egalitarianism does not arise systematically as an optimal outcome. In particular, in a growing economy, that is when population growth is optimal in the long-run, this egalitarian rule can only hold when the welfare function is Benthamite. When altruism is impure, egalitarianism is impossible in the context of a growing economy. Either in the Benthamite or impure altruism cases, procreation is never optimal for small enough life spans, leading to finite time extinction and maximal consumption for all existing individuals.

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  • Boucekkine, R. & Fabbri, G. & Gozzi, F., 2014. "Egalitarianism under population change: Age structure does matter," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 86-100.
    • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:86-100
    DOI: 10.1016/j.jmateco.2014.10.007
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    12. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
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    Cited by:

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    2. Stéphane Zuber, 2018. "Population-adjusted egalitarianism," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01937766, HAL.
    3. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
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    5. Méjean, Aurélie & Pottier, Antonin & Zuber, Stéphane & Fleurbaey, Marc, 2023. "Opposite ethical views converge under the threat of catastrophic climate change," Ecological Economics, Elsevier, vol. 212(C).
    6. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    7. Aurélie Méjean & Antonin Pottier & Marc Fleurbaey & Stéphane Zuber, 2020. "Catastrophic climate change, population ethics and intergenerational equity," Climatic Change, Springer, vol. 163(2), pages 873-890, November.
    8. Gregory Ponthiere, 2016. "Utilitarian population ethics and births timing," Journal of Economics, Springer, vol. 117(3), pages 189-238, April.
    9. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    10. Raouf Boucekkine & Blanca Martínez & J. Ramon Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 321-347, Springer.
    11. Marc Fleurbaey & Stéphane Zuber, 2021. "Universal social welfare orderings and risk," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03289160, HAL.
    12. Emmanuelle Augeraud-Veron & Mauro Bambi & Fausto Gozzi, 2017. "Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 584-611, May.
    13. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    14. Hu, Qiyu & Shen, Wencang & Yan, Jinming & Kong, Weilong & Li, Wei & Zhang, Zhengfeng, 2024. "Does existing mixed land development promote the urban spatial composite function? Evidence from Beijing, China," Land Use Policy, Elsevier, vol. 143(C).
    15. Augeraud-Véron, Emmanuelle & Fabbri, Giorgio & Schubert, Katheline, 2021. "Prevention and mitigation of epidemics: Biodiversity conservation and confinement policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    16. Nicholas Lawson & Dean Spears, 2018. "Optimal population and exhaustible resource constraints," Journal of Population Economics, Springer;European Society for Population Economics, vol. 31(1), pages 295-335, January.
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    18. Kohei Kamaga, 2016. "Infinite-horizon social evaluation with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 207-232, June.

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    More about this item

    Keywords

    Egalitarianism; Age structure; Total utilitarianism; Impure altruism; Endogenous growth;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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