General Pattern Formation in Recursive Dynamical Systems Models in Economics

Brock, William and Xepapadeas, Anastasios (2008): General Pattern Formation in Recursive Dynamical Systems Models in Economics.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Pattern formation, spatial spillovers, optimal control, spillover induced instability, growth models
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

AGHION, P., AND P. HOWITT (1992): "A Model of Growth Through Creative Destruction," Econometrica, 60, 323--351.

ATHANS, M., and P. FALB (1966): Optimal Control. New York: McGraw-Hill.

BALDWIN, R. (2001): "Core-Periphery Model with Forward-Looking Expectations," Regional Science and Urban Economics, 31, 21--49.

BALDWIN, R., AND P. MARTIN (2004): "Agglomeration and Regional Growth," in Handbook of Regional and Urban Economics, Part III, 60, ed. by V. Henderson, and J.F. Thisse. Amsterdam: North Holland.

BARRO, R. J., AND X. SALA-I-MARTIN (2004): Economic Growth, Second Edition. Cambridge, MA: MIT Press.

BOUCEKKINE, R., C. CAMACHO, AND B. ZOU (2006): "Bridging the Gap between Growth Theory and the New Economic Geography: The Spatial Ramsey Model," CORE Discussion Paper, 2006/72, Department of Economics, Catholic University of Louvain.

BROCK, W., AND A. MALLIARIS (1989): Differential Equations, Stability and Chaos in Dynamic Economics. Amsterdam: North-Holland.

BROCK, W., AND A. XEPAPADEAS (2008a): "Diffusion-Induced Instability and Pattern Formation in Infinite Horizon Recursive Optimal Control," Journal of Economic Dynamics and Control, 32, 2745--2787.

BROCK, W., AND A. XEPAPADEAS (2008b): "Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems," Working paper, Available at SSRN: http://ssrn.com/abstract=1144071.

CARLSON, D., A. HAURIE, AND A. LEIZAROWITZ (1991): Infinite Horizon Optimal Control, Second Edition. Berlin: Springer-Verlag.

CASS, D., AND K. SHELL (eds.) (1976): The Hamiltonian Approach to Dynamic Economics. New York: Academic Press.

CHINCARINI, L., AND N. ASHERIE (2008): "An Analytical Model for the Formation of Economic Clusters," Regional Science and Urban Economics, 38, 252--270.

DESMET, K., AND E. ROSSI-HANSBERG (2007): "Spatial Growth and Industry Age," CEPR Discussion Paper No. DP6421.

DIEUDONNE, J. (1969): Foundations of Modern Analysis. New York: Academic Press.

FUJITA, M., P. KRUGMAN, AND A. VENABLES (1999): The Spatial Economy. Cambridge, MA: The MIT Press.

GROSSMAN, G. M., AND E. HELPMAN (1991a): Innovation and Growth in the Global Economy. Cambridge, MA: MIT Press.

GROSSMAN, G. M., AND E. HELPMAN (1991b): "Quality Ladders and Product Cycles," Quarterly Journal of Economics, 106, 557-586.

IOANNIDES, Y. M., AND H. G. OVERMAN (2007): "Spatial Evolution and the U.S. Urban System," Journal of Economic Geography, 4, 131--156.

JONES, C. I. (1995): "R&D-Based Models of Economic Growth," Journal of Political Economy, 103, 759--784.

KAMIEN, M., AND N. SCHWARTZ (1981): Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Second Edition. New York: North-Holland.

KRUGMAN, P. (1996): The Self-Organizing Economy. Cambridge, MA: Blackwell Publishers.

KURZ, M. (1968): "The General Instability of a Class of Competitive Growth Processes," Review of Economic Studies, 35, 155--174.

LEIZAROWITZ, A. (2008): "Turnpike properties of a class of aquifer control problems," Automatica, 44, 1460--1470.

LUCAS, R. E. (1988): "On the Mechanics of Economic Development," Journal of Monetary Economics, 22 (1), 3--42.

LUCAS, R. E. (2001): "Externalities and Cities," Review of Economic Dynamics, 4, 245--274.

LUCAS, R. E., AND E. ROSSI-HANSBERG (2002): "On the Internal Structure of Cities," Econometrica, 70(4), 1445--1476.

MARTIN, R., AND P. SUNLEY (2003): "Deconstructing Clusters: Chaotic Concept or Policy Panacea?" Journal of Economic Geography, 3, 5--35.

MATSUYAMA, K. (2008a): "Structural Change," in The New Palgrave, ed. by L. Blume, and S. Durlauf. London: McMillan

MATSUYAMA, K. (2008b): "Symmetry Breaking," in The New Palgrave, ed. by L. Blume, and S. Durlauf. London: McMillan.

MCKENZIE, L. (1983): "Optimal Economic Growth and Turnpike Theorems," in The Handbook of Mathematical Economics, Volume 3, ed. by K. Arrow, and M. Intriligator. Amsterdam: North Holland.

MOISEIWITSCH, B. L. (2005): Integral Equations. Dover Publications.

MOSSAY, P. (2006): "A Theory of Rational Spatial Agglomerations," Department of Economics, University of Alicante.

MURRAY, J. (2002): Mathematical Biology, Volume I, Third Edition. Berlin: Springer.

MURRAY, J. (2003): Mathematical Biology, Volume II, Third Edition. Berlin: Springer.

OKUBO, A., AND S. LEVIN (Eds) (2001): Diffusion and Ecological Problems: Modern Perspectives, 2nd Edition. Berlin: Springer.

OTTAVIANO, G. (2001): "Monopolistic Competition, Trade, and Endogenous Spatial Fluctuations," Regional Science and Urban Economics, 31, 51--77.

PORTER, D., AND D. S. G. STIRLING (1990): Integral Equations. Cambridge: Cambridge University Press.

PRIESTLEY, M. (1981): Spectral Analysis and Time Series, Vol. 1. London: Academic Press.

QUAH, D. (2002): "Spatial Agglomeration Dynamics," AEA Papers and Proceedings, 92, 247--252.

ROMER, P. M. (1986): "Increasing Returns and Long-Run Growth," Journal of Political Economy, 94 (5), 1002--10037.

ROMER, P. M. (1990): "Endogenous Technological Change," Journal of Political Economy, 98, S71--S102.

SCHEINKMAN, J. (1976): "On Optimal Steady States of N-Sector Growth Models When Utility Is Discounted," Journal of Economic Theory, 12, 11--30.

SOLOW, R. (1956): "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, 70, 65--94.

STOKEY, N. L., R. E. LUCAS WITH E. C. PRESCOTT (1989): Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press.

TURING, A. (1952): "The Chemical Basis of Morphogenesis," Philosophical Transactions of the Royal Society of London, 237, 37--72.