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Optimal Agglomerations in Dynamic Economics

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Listed author(s):
  • Athanasios Yannacopoulos
  • Anastasios Xepapadeas
  • William Brock

Abstract

We study rational expectations equilibrium problems and social optimum problems in infinite 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 infinite dimensional Hilbert spaces. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics.

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File URL: http://wpa.deos.aueb.gr/docs/BXY.Optima.Agglomerations.5.July.pdf
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Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1217.

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Handle: RePEc:aue:wpaper:1217
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Keywords: Agglomeration; spatial spillovers; spillover induced instability; rational expectations equilibrium; social optimum; monotone operators.;

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Find related papers by JEL classification:
  • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
  • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

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  1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
  2. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
  3. 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.
  4. 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.
  5. Benteng Zou & Carmen Camacho, 2004. "The spatial Solow model," Economics Bulletin, AccessEcon, vol. 18(2), pages 1-11.
  6. Lionel W. McKenzie, 2012. "turnpike theory," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  7. Grossman, Gene M. & Helpman, Elhanan, 1991. "Trade, knowledge spillovers, and growth," European Economic Review, Elsevier, vol. 35(2-3), pages 517-526, April.
  8. Robert E. Lucas, Jr., 2001. "Externalities and Cities," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(2), pages 245-274, April.
  9. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
  10. Nocco, Antonella, 2005. "The rise and fall of regional inequalities with technological differences and knowledge spillovers," Regional Science and Urban Economics, Elsevier, vol. 35(5), pages 542-569, September.
  11. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
  12. 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.
  13. 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.
  14. Danny Quah, 2002. "Spatial agglomeration dynamics," LSE Research Online Documents on Economics 2042, London School of Economics and Political Science, LSE Library.
  15. Fujita, Masahisa & Hamaguchi, Nobuaki, 2001. "Intermediate goods and the spatial structure of an economy," Regional Science and Urban Economics, Elsevier, vol. 31(1), pages 79-109, February.
  16. José Alexandre Scheinkman, 1978. "Stability of Separable Hamiltonians and Investment Theory," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 559-570.
  17. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  18. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 252-270, May.
  19. Desmet, Klaus & Rossi-Hansberg, Esteban, 2009. "Spatial growth and industry age," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2477-2502, November.
  20. Danny Quah, 2002. "Spatial Agglomeration Dynamics," CEP Discussion Papers dp0521, Centre for Economic Performance, LSE.
  21. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
  22. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75, pages 321-321.
  23. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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Cited by:

  1. Simon Levin & A. Xepapadeas, 2015. "Transboundary Capital and Pollution Flows and the Emergence of Regional Inequalities," Working Papers 2015.69, Fondazione Eni Enrico Mattei.
  2. Anastasios Xepapadeas & Athanasios Yannacopoulos & Andreas Ioannidis, 2014. "Spatial Growth: The Distribution of Capital across Locations when Saving Rates are Exogenous," DEOS Working Papers 1412, Athens University of Economics and Business.
  3. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, "undated". "Adjustment Costs and Long Run Spatial Agglomerations," DEOS Working Papers 1327, Athens University of Economics and Business.
  4. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
  5. 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, vol. 37(12), pages 2371-2396.

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