IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-08c60002.html
   My bibliography  Save this article

The Solow model in discrete time and decreasing population growth rate

Author

Listed:
  • Juan Sebastián Pereyra

    (Universidad de la República)

  • Juan Gabriel Brida

    (Free University of Bolzano)

Abstract

This paper reformulates the neoclassical Solow-Swan model of economic growth in discrete time by introducing a generic population growth law that verifies the following properties: 1) population is strictly increasing and bounded 2) the rate of growth of population is decreasing to zero as time tends to infinity. We show that in the long run the capital per worker of the model converges to the non-trivial steady state of the Solow Swan model with zero labor growth rate. In addition we prove that the solutions of the model are asymptotically stable.

Suggested Citation

  • Juan Sebastián Pereyra & Juan Gabriel Brida, 2008. "The Solow model in discrete time and decreasing population growth rate," Economics Bulletin, AccessEcon, vol. 3(41), pages 1-14.
    • Handle: RePEc:ebl:ecbull:eb-08c60002
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/EB/2008/Volume3/EB-08C60002A.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. Pasquale Commendatore, 2004. "Complex dynamics in a Pasinetti-Solow model of Growth and distribution," Computing in Economics and Finance 2004 279, Society for Computational Economics.
    4. Guerrini, Luca, 2006. "The Solow-Swan model with a bounded population growth rate," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 14-21, February.
    5. Brianzoni Serena & Mammana Cristiana & Michetti Elisabetta, 2007. "Complex Dynamics in the Neoclassical Growth Model with Differential Savings and Non-Constant Labor Force Growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-19, September.
    6. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    7. Luis A. Puch & Omar Licandro, 2006. "Is Discrete Time a Good Representation of Continuous Time?," Working Papers 2006-20, FEDEA.
    8. Erick José Limas Maldonado & Juan Gabriel Brida, 2005. "Closed form solutions to a generalization of the Solow growth model," GE, Growth, Math methods 0510003, University Library of Munich, Germany.
    9. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    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. Marsiglio, Simone & La Torre, Davide, 2012. "Population dynamics and utilitarian criteria in the Lucas–Uzawa Model," Economic Modelling, Elsevier, vol. 29(4), pages 1197-1204.

    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. repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
    2. Fabio Tramontana & Viktor Avrutin, 2014. "Complex endogenous dynamics in a one-sector growth model with differential savings," DEM Working Papers Series 078, University of Pavia, Department of Economics and Management.
    3. Dohtani, Akitaka, 2010. "A growth-cycle model of Solow-Swan type, I," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 428-444, November.
    4. João Juchem Neto & Julio Claeyssen, 2015. "Capital-induced labor migration in a spatial Solow model," Journal of Economics, Springer, vol. 115(1), pages 25-47, May.
    5. Tramontana, Fabio & Gardini, Laura & Agliari, Anna, 2011. "Endogenous cycles in discontinuous growth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1625-1639.
    6. Serena Brianzoni, & Cristiana Mammana, & Elisabetta Michetti,, 2006. "Global attractor in Solow growth model with differential savings and endogenic labor force growth," Working Papers 35-2006, Macerata University, Department of Finance and Economic Sciences, revised Oct 2008.
    7. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2009. "Nonlinear dynamics in a business-cycle model with logistic population growth," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 717-730.
    8. Grassetti, F. & Guzowska, M. & Michetti, E., 2020. "A dynamically consistent discretization method for Goodwin model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    10. Michetti, Elisabetta, 2015. "Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 215-232.
    11. Akio Matsumoto & Ferenc Szidarovszky, 2013. "Asymptotic Behavior of a Delay Differential Neoclassical Growth Model," Sustainability, MDPI, vol. 5(2), pages 1-16, January.
    12. Nicol`o Cangiotti & Mattia Sensi, 2020. "Exact solutions for a Solow-Swan model with non-constant returns to scale," Papers 2008.05875, arXiv.org.
    13. Juchem Neto, J.P. & Claeyssen, J.C.R. & Pôrto Júnior, S.S., 2018. "Economic agglomerations and spatio-temporal cycles in a spatial growth model with capital transport cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 76-86.
    14. Francesca Grassetti & Cristiana Mammana & Elisabetta Michetti, 2018. "Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 145-162, November.
    15. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    16. David Cheban & Cristiana Mammana & Elisabetta Michetti, 2012. "Non-Autonomous Difference Equations: Global Attractor in a Business-Cycle Model with Endogenous Population Growth," Working Papers 69-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.
    17. Agliari, Anna & Böhm, Volker & Pecora, Nicolò, 2020. "Endogenous cycles from income diversity, capital ownership, and differential savings," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    18. Bohm, Volker & Kaas, Leo, 2000. "Differential savings, factor shares, and endogenous growth cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 965-980, June.
    19. Akio Matsumoto & Ferenc Szidarovszky, 2021. "Delay two-sector economic growth model with a Cobb–Douglas production function," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 341-358, June.
    20. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2012. "Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 98-108.
    21. Serena Brianzoni & Raffaella Coppier & Elisabetta Michetti, 2015. "Multiple equilibria in a discrete time growth model with corruption in public procurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2387-2410, November.

    More about this item

    Keywords

    Solow model;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

    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:ebl:ecbull:eb-08c60002. 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: John P. Conley (email available below). General contact details of provider: .

    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.