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The Dynamics of Growth and Distribution in a Spatially Heterogeneous World

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  • Paulo Brito

Abstract

This paper tries to reconcile growth and geographical economics by dealing directly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson- Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation.

Suggested Citation

  • 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.
  • Handle: RePEc:ise:isegwp:wp142004
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    2. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    3. 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.
    4. Gani Aldashev & Serik Aldashev & Timoteo Carletti, 2014. "On Convergence in the Spatial AK Growth Models," Papers 1401.4887, arXiv.org.
    5. Breinlich, Holger & Ottaviano, Gianmarco I.P. & Temple, Jonathan R.W., 2014. "Regional Growth and Regional Decline," Handbook of Economic Growth,in: Handbook of Economic Growth, edition 1, volume 2, chapter 4, pages 683-779 Elsevier.
    6. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    7. Grames, Johanna & Grass, Dieter & Kort, Peter M. & Fürnkranz-Prskawetz, Alexia, 2017. "Optimal investment and location decisions of a firm in a flood risk area using Impulse Control Theory," ECON WPS - Vienna University of Technology Working Papers in Economic Theory and Policy 01/2017, Vienna University of Technology, Institute for Mathematical Methods in Economics, Research Group Economics (ECON).
    8. Raouf Boucekkine & Carmen Camacho & Fabbri Giorgio, 2013. "On the optimal control of some parabolic partial differential equations arising in economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00973388, HAL.
    9. Giorgio Fabbri, 2015. "Ecological barriers and convergence: a note on geometry in spatial growth models," Working Papers hal-01159253, HAL.
    10. W. Brock & A. Xepapadeas & A. Yannacopoulos, 2014. "Robust Control and Hot Spots in Spatiotemporal Economic Systems," Dynamic Games and Applications, Springer, vol. 4(3), pages 257-289, September.
    11. Raouf BOUCEKKINE & Giorgio FABBRI & Salvatore FEDERICO & Fausto GOZZI, 2017. "Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017006, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    12. 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.
    13. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    14. 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.
    15. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
    16. Juchem Neto, Joao Plinio & Claeyssen, Julio Cesar Ruiz & Porto Junior, Sabino da Silva, 2014. "A spatial Solow model with transport cost," MPRA Paper 59766, University Library of Munich, Germany.
    17. Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
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    19. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    20. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics," Working Papers halshs-00831042, HAL.
    21. 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.

    More about this item

    Keywords

    Optimal growth and distribution; Spatial growth; Optimal control of partial differential equations; Traveling waves; Fourier transforms; Turing instability.;

    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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