Akamatsu, Takashi and Takayama, Yuki and Ikeda, Kiyohiro (2009): Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models.

PDF
MPRA_paper_21738.pdf Download (653kB)  Preview 
Abstract
We provide an analytical approach that facilitates understanding the bifurcation mechanism of a wide class of economic models involving spatial agglomeration of economic activities. The proposed method overcomes the limitations of the Turing (1952) approach that has been used to analyze the emergence of agglomeration in the multiregional coreperiphery (CP) model of Krugman (1993, 1996). In other words, the proposed method allows us to examine whether agglomeration of mobile factors emerges from a uniform distribution and to analytically trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as a uniform pattern) that these models exhibit when the values of some structural parameters change steadily. Applying the proposed method to the multiregional CP model, we uncover a number of previously unknown properties of the CP model, and notably, the occurrence of “spatial period doubling bifurcation” in the CP model is proved.
Item Type:  MPRA Paper 

Original Title:  Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models 
Language:  English 
Keywords:  economic geography; agglomeration; stability; bifurcation; gravity laws 
Subjects:  F  International Economics > F1  Trade > F15  Economic Integration F  International Economics > F2  International Factor Movements and International Business > F22  International Migration R  Urban, Rural, Regional, Real Estate, and Transportation Economics > R1  General Regional Economics > R13  General Equilibrium and Welfare Economic Analysis of Regional Economies C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools F  International Economics > F1  Trade > F12  Models of Trade with Imperfect Competition and Scale Economies ; Fragmentation R  Urban, Rural, Regional, Real Estate, and Transportation Economics > R1  General Regional Economics > R12  Size and Spatial Distributions of Regional Economic Activity C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  21738 
Depositing User:  Yuki Takayama 
Date Deposited:  31. Mar 2010 05:45 
Last Modified:  14. May 2015 11:36 
References:  Akamatsu, T. and Takayama, Y. (2009a): “A Simplified Approach to Analyzing Multiregional Core Periphery Models,” TUTUP Working Paper, Tohoku University. Akamatsu, T. and Takayama, Y. (2009b): “Dispersion Forces Matter for the Emergence of Polycentric Urban Configurations,” TUTUP Working Paper, Tohoku University. Akamatsu, T., Takayama, Y. and Sugasawa, A. (2009): “Market Territories and Agglomeration Patterns in a CorePeriphery System of Cities Model,” TUTUP Working Paper, Tohoku University. Anas, A. (1983): “Discrete Choice Theory, Information Theory, and the Multinomial Logit and Gravity Models,” Transportation Research B, 17, 1323. Anderson, J. (1979): “A Theoretical Foundation for the Gravity Equation,” American Economic Review, 69, 106116. Anderson, J. and van Wincoop, E. (2003): “Gravity with Gravitas, A Solution to the Border Puzzle,”American Economic Review, 93, 170192. Anderson, S.P., de Palma, A. and Thisse, J.F. (1992): Discrete Choice Theory of Product Differentiation, MIT Press. Baldwin, R., Forslid, R., Martin, P., Ottaviano, G. and RobertNicoud, F. (2003): Economic Geography and Public Policy, Princeton University Press. Behrens, K. and Thisse, J.F. (2007): “Regional Economics, A New Economic Geography Perspective,” Regional Science and Urban Economics, 37, 457465. Bergstrand, J.H. (1989): “The Generalized Gravity Equation, Monopolistic Competition, and the FactorProportions Theory in International Trade,” Review of Economics and Statistics, 71, 143153. Berliant, M., Peng, S.K. and Wang, P. (2002): “Production Externalities and Urban Configuration,”Journal of Economic Theory, 104, 275303. Berliant, M. and Wang, P. (2008): “Urban Growth and Subcenter Formation: A Trolley Ride from the Staples Center to Disneyland and the Rose Bowl,” Journal of Urban Economics, 63, 679693. Christaller, W. (1933): Central Places in Southern Germany, In Charles W. Baskin (trans.) Die Zentralen Orte in Süddeutschland. Englewood Cliffs, NJ: Prentice Hall. Combes, PP., Mayer, T. and Thisse, JF. (2008): Economic Geography: The Integration of Regions and Nations, Princeton University Press. Dixit, A. and Stiglitz, J. (1977): “Monopolistic Competition and Optimum Product Diversity,”American Economic Review, 67, 297308. Eaton, B.C. and Wooders, M.H. (1985): “Sophisticated Entry in a Model of Spatial Competition,”RAND Journal of Economics, 16, 282297. Evenett, S. and Keller, W. (2002): “On Theories Explaining the Success of the Gravity Equation,”Journal of Political Economy, 110, 281316. Flam, H. and Helpman, E. (1987): “Industrial Policy under Monopolistic Competition,” Journal of International Economics, 22, 79102. Forslid, R. and Ottaviano, G. (2003): “An Analytically Solvable Core Periphery Model,” Journal of Economic Geography, 3, 229240. Fudenberg, D. and Levine, D. K., (1998): The Theory of Learning in Games, MIT Press. Fujita, M. (1988): “A Monopolistic Competition Model of Spatial Agglomeration: Differentiated Product Approach,” Regional Science and Urban Economics, 18, 87124. Fujita, M. and Mori, T., (1997): “Structural Stability and Evolution of Urban Systems,” Regional Science and Urban Economics, 27, 399442. Fujita, M. Krugman, P., and Venables, A.J. (1999): The Spatial Economy, MIT Press. Fujita, M. and Ogawa, H. (1982): Multiple Equilibria and Structural Transition of Nonmonocentric Urban Configurations, Regional Science and Urban Economics, 12, 161196. Fujita, M. and Thisse, J.F. (2002): Economics of Agglomeration, Cambridge University Press. Fujita, M. and Thisse, J.F. (2009): “New Economic Geography: An Appraisal on the Occasion of Paul Krugman’s 2008 Nobel Prize in Economic Sciences,”Regional Science and Urban Economics, 39, 109119. Glaeser, E.L. (2008): Cities, Agglomeration and Spatial Equilibrium, Oxford University Press. Golubitsky, M. and Schaeffer, D.G. (1985): Singularities and Groups in Bifurcation Theory, Springer. Gray, R. M. (2006): “Toeplitz and Circulant Matrices: A Review,” Foundations and Trends in Communications and Information Theory, 2, 155239. Hale, J. and Kocak, H. (1991): Dynamics and Bifurcations, Springer. Helpman, E. (1998): “The Size of Regions,” in Pines, D., Sadka, E. and Zilcha Y. (eds.), Topics in Public Economics. Theoretical and Applied Analysis, Cambridge University Press, 3354. Henderson, J.V. and Thisse, J.F.(eds.) (2004): Handbook of Regional & Urban Economics, 4, Elsevier. Hirsch, M.W. and Smale, S. (1974): Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press. Hofbauer, J. and Sandholm, W. H. (2002): “On the Global Convergence of Stochastic Fictitious Play,”Econometrica, 70, 22652294. Hofbauer, J. and Sandholm, W. H. (2007): “Evolution in Games with Randomly Disturbed Payoffs,”Journal of Economic Theory, 132, 4769. Ikeda, K., Akamatsu, T. and Kono, T. (2009): “Spatial Agglomeration Pattern of a System of Cities: Bifurcation Theory for CorePeriphery Model,” TUTUP Working Paper, Tohoku University. Krugman, P. (1991): “Increasing Returns and Economic Geography,” Journal of Political Economy, 99, 483499. Krugman, P. (1993): “On the Number and Location of Cities,” European Economic Review, 37, 293298. Krugman, P. (1996): The SelfOrganizing Economy, Blackwell Publishers. Lucas, R.E. and RossiHansberg, E. (2002): “On the Internal Structure of Cities,” Econometrica, 77, 14451476. Martin, P.J. and Rogers, C.A. (1995): “Trade Effects of Regional Aid,” in Baldwin, R., Haaparanta, P. and Kiander, J. (eds.), Expanding Membership of the European Union, Cambridge University Press, 166188. McFadden, D. (1974): “Conditional Logit Analysis of Qualitative Choice Behavior,” in Zarembka, P. (eds.), Frontiers in Econometrics, Academic Press, 105142. Mossay, P. (2003): “Increasing Returns and Heterogeneity in a Spatial Economy,” Regional Science and Urban Economics, 33, 419444. Murata, Y. (2003): “Product Diversity, Taste Heterogeneity, and Geographic Distribution of Economic Activities: Market vs. Nonmarket Interactions,” Journal of Urban Economics, 53, 126144. Novshek, W. (1980): “Equilibrium in Simple Spatial (or Differentiated Product) Models,” Journal of Economic Theory, 22, 313326. Ottaviano, G., Tabuchi, T. and Thisse, J.F. (2002): “Agglomeration and Trade Revisited,”International Economic Review, 43, 409436. Oyama, D. (2009). “Agglomeration under Forwardlooking Expectations: Potentials and Global Stability,” Regional Science and Urban Economics, 39, 696713. Papageorgiou, Y.Y. and Smith, T.R. (1983): “Agglomeration as Local Instability of Spatially Uniform SteadyStates,” Econometrica, 51, 11091120. Picard, P.M. and Tabuchi, T. (2009): “SelfOrganized Agglomerations and Transport Costs,” Economic Theory, 42, 565589. Pflüger, M. (2004): “A Simple Analytically Solvable, Chamberlinian Agglomeration Model,” Regional Science and Urban Economics, 34, 565573. Ravenstein, E.G. (1885): “The Laws of Migration,” Journal of the Royal Statistical Society, 48, 167227. Reilly, W.J. (1931): The Law of Retail Gravitation, Knickerbrocker Press. Sandholm, W.H. (2009): Population Games and Evolutionary Dynamics, MIT Press. Salop, S. (1979): “Monopolistic Competition with Outside Goods,” Bell Journal of Economics, 10, 141156. Sen, A.K. and Smith, T.E. (1995): Gravity Models of Spatial Interaction Behavior, Springer. Smith, T.E. (1976): “Spatial Discounting and the Gravity Hypothesis,”Regional Science and Urban Economics, 6, 331356. Tabuchi, T. (1998): “Urban Agglomeration and Dispersion: A Synthesis of Alonso and Krugman,”Journal of Urban Economics, 44, 333351. Tabuchi, T., Thisse, J.F. and Zeng, D.Z. (2005): “On the Number and Size of Cities,” Journal of Economic Geography, 5, 423448. Tabuchi, T., and Thisse, J.F. (2009): “Selforganizing Urban Hierarchy,” CIRJE discussion paper, No.F414, University of Tokyo. Tinbergen, J. (1962): Shaping the World Economy: Suggestions for an International Economic Policy, Twentieth Century Fund. Turing, A.M. (1952): “The Chemical Basis of Morphogenesis,” Philosophical Transactions of the Royal Society of London, 237, 3772. Van Loan, C. (1992): Computational Frameworks for the Fast Fourier Transform, SIAM. Voorhees, A.M. (1955): “A General Theory of Traffic Movement,” Proceedings of the Institute of Traffic Engineers, 4656. Wilson, A.G. (1970): Entropy in Urban and Regional Modeling, Pion. Young, E.C. (1924): “The Movement of Farm Population,” Cornell Agricultural Experimental Station, Bulletin 426. Zipf, G.K. (1946): “The P1 P2/D Hypothesis: On the Intercity Movement of Persons,” American Sociological Review, 11, 677686. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/21738 