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Optimal Agglomerations in Dynamic Economics

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  • William Brock
  • Anastasios Xepapadeas
  • Athanasios Yannacopoulos

Abstract

We study rational expectations equilibrium problems and social optimum problems in in nite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in in nite dimensional Hilbert spaces. We show that agglomerations may emerge, with any type of returns to scale (increasing or decreasing) and with the marginal productivity of private capital increasing or decreasing with respect to the spatial externality. This is a fairly general result indicating the importance of the network structure of the spatial externality relative to the properties of the aggregate production function. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics.

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Bibliographic Info

Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1403.

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Date of creation: 01 Apr 2014
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Handle: RePEc:aue:wpaper:1403

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Keywords: Agglomeration; spatial spillovers; spillover induced instability; rational expectations equilibrium; social optimum; monotone operators.;

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  1. Scheinkman, Jose Alexandre, 1978. "Stability of Separable Hamiltonians and Investment Theory," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 45(3), pages 559-70, October.
  2. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 38(3), pages 252-270, May.
  3. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827641, HAL.
  4. BOUCEKKINE, Raouf & CAMACHO, Carmen & ZOU, Benteng, . "Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2090, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. Carmen Camacho & Benteng Zou & Maya Briani, 2005. "On the dynamics of capital accumulation across space," Working Papers 376, Bielefeld University, Center for Mathematical Economics.
  7. Carmen, CAMACHO & Benteng, ZOU, 2003. "The Spatial Solow Model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2003017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  8. Nocco, Antonella, 2005. "The rise and fall of regional inequalities with technological differences and knowledge spillovers," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 35(5), pages 542-569, September.
  9. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 75, pages 321.
  10. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
  11. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  12. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(5), pages 1002-37, October.
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Cited by:
  1. Brock, William A. & Engström, Gustav & Grass, Dieter & Xepapadeas, Anastasios, 2013. "Energy balance climate models and general equilibrium optimal mitigation policies," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 37(12), pages 2371-2396.
  2. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, . "Adjustment Costs and Long Run Spatial Agglomerations," DEOS Working Papers 1327, Athens University of Economics and Business.

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