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The diffusion of economic activity across space: a new approach

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  • Carmen Camacho

    () (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

  • Agustín Pérez-Barahona

    () (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

Abstract

Dynamic spatial theory has been a fruitful approach to understand economic phenomena involving time and space. However, this new field has opened a set of questions still unresolved in the literature. For instance, the identification of the social optimal allocation of economic activity across time and space has not been ensured yet in economic growth. By means of a monotone method, we study in this paper the optimal solution of spatial Ramsey-type models. We analytically prove, under fairly general assumptions, the existence of a unique social optimum. The iterative nature of this approach also allows us to present a new algorithm to simulate the optimal trajectories of the economy. We provide two economic illustrations of our method. Firstly, we apply our existence result to the spatial growth model and to a framework for optimal land-use planning, concluding that these problems are well-posed. We then consider the spatial growth model in order to investigate the importance of capital mobility in economic growth. We particularly underline the spatial dynamic implications of this feature on social welfare and income inequality.

Suggested Citation

  • Carmen Camacho & Agustín Pérez-Barahona, 2017. "The diffusion of economic activity across space: a new approach," PSE Working Papers halshs-01670532, HAL.
  • Handle: RePEc:hal:psewpa:halshs-01670532
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01670532
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    References listed on IDEAS

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    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. Kehoe, Timothy J. & Levine, David K. & Romer, Paul M., 1990. "Determinacy of equilibria in dynamic models with finitely many consumers," Journal of Economic Theory, Elsevier, vol. 50(1), pages 1-21, February.
    4. Desmet, Klaus & Rossi-Hansberg, Esteban, 2015. "On the spatial economic impact of global warming," Journal of Urban Economics, Elsevier, vol. 88(C), pages 16-37.
    5. Bental, Benjamin, 1985. "Is Capital Mobility Always Desirable? A Welfare Analysis of Portfolio Autarky in a Growing Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 203-212, February.
    6. Raj Chetty, 2006. "A New Method of Estimating Risk Aversion," American Economic Review, American Economic Association, vol. 96(5), pages 1821-1834, December.
    7. 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.
    8. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics," AMSE Working Papers 1334, Aix-Marseille School of Economics, Marseille, France, revised 05 Jun 2013.
    9. Adrien Blanchet & Pascal Mossay & Filippo Santambrogio, 2016. "Existence And Uniqueness Of Equilibrium For A Spatial Model Of Social Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 31-60, February.
    10. Baldwin, Richard E. & Krugman, Paul, 2004. "Agglomeration, integration and tax harmonisation," European Economic Review, Elsevier, vol. 48(1), pages 1-23, February.
    11. Klaus Desmet & Esteban Rossi-Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63.
    12. 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.
    13. 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.
    14. 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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    Keywords

    Control; Spatial dynamics; Ramsey model; Partial differential equations;

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