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General Pattern Formation in Recursive Dynamical Systems Models in Economics

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  • Brock, William
  • Xepapadeas, Anastasios

Abstract

This paper presents a fairly general treatment of recursive infinite horizon forward looking optimizing systems on infinite dimensional spatial domains. It includes optimal control, an analysis of local stability of spatially flat optimal steady states and development of techniques to compute spatially heterogeneous optimal steady states. The paper also develops a concept of rational expectations equilibrium, a local stability analysis for spatially homogeneous rational expectations steady states, and computational techniques for spatially heterogeneous rational expectations steady states.

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File URL: http://mpra.ub.uni-muenchen.de/12305/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12305.

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Date of creation: 20 Dec 2008
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Handle: RePEc:pra:mprapa:12305

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Keywords: Pattern formation; spatial spillovers; optimal control; spillover induced instability; growth models;

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References

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  1. Yannis M. Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 131-156, April.
  2. Raouf, BOUCEKKINE & Carmen, CAMACHO & Benteng, ZOU, 2006. "Bridging the Gap between Growth Theory and the New Economic Geography : The Spatial Ramsey Model," Discussion Papers (ECON - Département des Sciences Economiques) 2006038, Université catholique de Louvain, Département des Sciences Economiques.
  3. Gianmarco Ottaviano, 1996. "Monopolistic Competition, Trade and Endogenous Spatial Fluctuations," Working Papers 240, Dipartimento Scienze Economiche, Universita' di Bologna.
  4. Gene M. Grossman & Elhanan Helpman, 1989. "Quality Ladders and Product Cycles," NBER Working Papers 3201, National Bureau of Economic Research, Inc.
  5. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  6. 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.
  7. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
  8. Brock, William & Xepapadeas, Anastasios, 2008. "Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems," MPRA Paper 9105, University Library of Munich, Germany.
  9. Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc.
  10. McKenzie, Lionel W., 1979. "Optimal Economic Growth and Turnpike Theorems," Working Papers 267, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. Desmet, Klaus & Rossi-Hansberg, Esteban, 2009. "Spatial growth and industry age," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2477-2502, November.
  12. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
  13. 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.
  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.
  15. Baldwin, Richard & Martin, Philippe, 2003. "Agglomeration and Regional Growth," CEPR Discussion Papers 3960, C.E.P.R. Discussion Papers.
  16. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
  17. Paul Romer, 1991. "Endogenous Technological Change," NBER Working Papers 3210, National Bureau of Economic Research, Inc.
  18. Ron Martin & Peter Sunley, 2003. "Deconstructing clusters: chaotic concept or policy panacea?," Journal of Economic Geography, Oxford University Press, vol. 3(1), pages 5-35, January.
  19. Baldwin, Richard E., 2001. "Core-periphery model with forward-looking expectations," Regional Science and Urban Economics, Elsevier, vol. 31(1), pages 21-49, February.
  20. 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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Citations

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Cited by:
  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. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Documents de travail du Centre d'Economie de la Sorbonne 12012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Holger Breinlich & Gianmarco I. P. Ottaviano & Jonathan R. W. Temple, 2013. "Regional growth and regional decline," LSE Research Online Documents on Economics 51575, London School of Economics and Political Science, LSE Library.
  4. repec:hal:journl:halshs-00674020 is not listed on IDEAS

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