IDEAS home Printed from https://ideas.repec.org/a/taf/raaexx/v18y2011i3p287-305.html
   My bibliography  Save this article

Revisiting the Optimal Population Size Problem under Endogenous Growth: Minimal Utility Level and Finite Life

Author

Listed:
  • Raouf Boucekkine
  • Giorgio Fabbri
  • Fausto Gozzi

Abstract

In this paper, we devise a social criterion in the spirit of the critical utility level of Blackorby-Donaldson (1984) to study an optimal population size problem in an endogenously growing economy populated by workers living a fixed amount of time and without capital accumulation. Population growth is endogenous. The problem is analytically solved, yielding closed-form solutions to optimal demographic and economic dynamics. It is shown that provided the economy is not driven to optimal finite time extinction, the optimal solution is egalitarian for appropriate choices of the critical utility levels: all individuals of any cohort are given the same consumption. The results obtained do not require any priori restriction of the values of the elasticity of intertemporal substitution unlike in several related papers.

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2011. "Revisiting the Optimal Population Size Problem under Endogenous Growth: Minimal Utility Level and Finite Life," Asia-Pacific Journal of Accounting & Economics, Taylor & Francis Journals, vol. 18(3), pages 287-305.
    • Handle: RePEc:taf:raaexx:v:18:y:2011:i:3:p:287-305
    DOI: 10.1080/16081625.2011.9720885
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/16081625.2011.9720885
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/16081625.2011.9720885?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    2. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    3. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
    4. repec:hal:wpaper:halshs-00536073_v1 is not listed on IDEAS
    5. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
    6. Palivos, Theodore, 2001. "Social norms, fertility and economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1919-1934, December.
    7. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    8. Oded Galor & Omer Moav, 2007. "The Neolithic Revolution and Contemporary Variations in Life Expectancy," Working Papers 2007-14, Brown University, Department of Economics.
    9. Razin, Assaf & Yuen, Chi-Wa, 1995. "Utilitarian Tradeoff between Population Growth and Income Growth," Journal of Population Economics, Springer;European Society for Population Economics, vol. 8(1), pages 81-87, February.
    10. Ng, Yew-Kwang, 1986. "Social criteria for evaluating population change: An alternative to the Blackorby-Donaldson criterion," Journal of Public Economics, Elsevier, vol. 29(3), pages 375-381, April.
    11. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
    12. Marc Nerlove & Assaf Razin & Efraim Sadka, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(2), pages 321-334.
    13. Blackorby, Charles & Donaldson, David, 1984. "Social criteria for evaluating population change," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 13-33, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
    2. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2012. "Egalitarism under Population Change. The Role of Growth and Lifetime Span," AMSE Working Papers 1211, Aix-Marseille School of Economics, France.
    3. 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.
    4. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    5. Raouf Boucekkine & Giorgio Fabbri, 2013. "Assessing Parfit’s Repugnant Conclusion within a canonical endogenous growth set-up," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(2), pages 751-767, April.
    6. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona School of Economics.
    7. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    8. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
    9. Marsiglio, Simone, 2014. "Reassessing Edgeworth’s conjecture when population dynamics is stochastic," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 130-140.
    10. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    11. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    12. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    13. Stelter, Robert, 2014. "Over-aging: Are present human populations too old?," Thuenen-Series of Applied Economic Theory 137, University of Rostock, Institute of Economics.
    14. 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.
    15. , B. & ,, 2014. "Escaping the repugnant conclusion: rank-discounted utilitarianism with variable population," Theoretical Economics, Econometric Society, vol. 9(3), September.
    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.
    17. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    18. d’Albis, Hippolyte & Augeraud-Veron, Emmanuelle & Venditti, Alain, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 295-308.
    19. Christoph Heinzel & Ralph Winkler, 2011. "Distorted Time Preferences and Time-to-Build in the Transition to a Low-Carbon Energy Industry," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 49(2), pages 217-241, June.
    20. Giorgio FABBRI, 2014. "Ecological Barriers and Convergence: a Note on Geometry in Spatial Growth Models," LIDAM Discussion Papers IRES 2014014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).

    More about this item

    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:taf:raaexx:v:18:y:2011:i:3:p:287-305. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/raae20 .

    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.