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Global Endogenous Growth and Distributional Dynamics


  • Paulo Brito


In this paper we deal with the global distribution of capital and output across time. We supply empirical support to model it as a partial differential equation, if the support of the distribution is related to an initial ranking of the economies. If we consider a distributional extension of the AK model we prove that it displays both global endogenous growth and transitional convergence in a distributional sense. This property can also be shared by a distributional extension of the Ramsey model. We conduct a qualitative analysis of the distributional dynamics and prove that If the technology displays mild decreasing marginal returns we can have long run growth if a diffusion induced bifurcation is crossed. This means that global growth can exist even in the case in which the local production functions are homogeneous and display decreasing returns to scale.

Suggested Citation

  • Paulo Brito, 2012. "Global Endogenous Growth and Distributional Dynamics," DEGIT Conference Papers c017_053, DEGIT, Dynamics, Economic Growth, and International Trade.
  • Handle: RePEc:deg:conpap:c017_053

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    References listed on IDEAS

    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(01), pages 20-45, February.
    3. Jaume Ventura & Francesco Caselli, 2000. "A Representative Consumer Theory of Distribution," American Economic Review, American Economic Association, vol. 90(4), pages 909-926, September.
    4. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," Review of Economic Studies, Oxford University Press, vol. 32(3), pages 233-240.
    5. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753, March.
    6. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
    7. Klaus Desmet & Esteban Rossi-Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63.
    8. Robert E. Lucas, 2009. "Trade and the Diffusion of the Industrial Revolution," American Economic Journal: Macroeconomics, American Economic Association, vol. 1(1), pages 1-25, January.
    9. Chatterjee, Satyajit, 1994. "Transitional dynamics and the distribution of wealth in a neoclassical growth model," Journal of Public Economics, Elsevier, vol. 54(1), pages 97-119, May.
    10. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    11. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
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    Cited by:

    1. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Spatial externalities and agglomeration in a competitive industry," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 143-174.
    2. Giorgio Fabbri, 2015. "Ecological barriers and convergence: a note on geometry in spatial growth models," Working Papers hal-01159253, HAL.
    3. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    4. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Optimal agglomerations in dynamic economics," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 1-15.
    5. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.

    More about this item


    optimal control of parabolic PDE; endogenous growth; diffusion induced bifurcation;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics


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