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Spatial dynamics and convergence: the spatial AK model

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  • Raouf Boucekkine
  • Carmen Camacho
  • Giorgio Fabbri

Abstract

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Despite constant returns to capital, we prove that transition dynamics will set in. In particular, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.

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Bibliographic Info

Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2010_06.

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Date of creation: Mar 2010
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Handle: RePEc:gla:glaewp:2010_06

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Keywords: Economic Growth; Inequality; Spatial Dynamics; Convergence;

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References

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  1. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  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. 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.
  4. 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.
  5. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
  6. Silvia Faggian, 2008. "Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital," Working Papers 181, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  7. Klaus Desmet & Esteban Rossi-Hansberg, 2009. "On Spatial dynamics," Working Papers 2009-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
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Cited by:
  1. repec:hal:wpaper:halshs-00831042 is not listed on IDEAS
  2. Athanasios Yannacopoulos & Anastasios Xepapadeas & William Brock, . "Optimal Agglomerations in Dynamic Economics," DEOS Working Papers 1217, Athens University of Economics and Business.
  3. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
  4. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.
  5. repec:hal:cesptp:halshs-00831042 is not listed on IDEAS
  6. Raouf Boucekkine & Giorgio Fabbri & Patrick-Antoine Pintus, 2011. "On the optimal control of a linear neutral differential equation arising in economics," Working Papers halshs-00576770, HAL.
  7. 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.
  8. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00674020, HAL.
  9. repec:hal:journl:halshs-00674020 is not listed on IDEAS
  10. Gani Aldashev & Serik Aldashev & Timoteo Carletti, 2014. "On Convergence in the Spatial AK Growth Models," Papers 1401.4887, arXiv.org.
  11. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the optimal control of some parabolic partial differential equations arising in economics," Documents de recherche 13-10, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.

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