A Simplified Approach to Analyzing Multi-regional Core-Periphery Models

Akamatsu, Takashi and Takayama, Yuki (2009): A Simplified Approach to Analyzing Multi-regional Core-Periphery Models.

Abstract

This paper shows that the evolutionary process of spatial agglomeration in multi-regional core-periphery models can be explained analytically by a much simpler method than the continuous space approach of Krugman (1996). The proposed method overcomes the limitations of Turing's approach which has been applied to continuous space models. In particular, it allows us not only to examine whether or not agglomeration of mobile factors emerges from a uniform distribution, but also to trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as from a uniform pattern) with decreases in transportation cost.

• Item Type: MPRA Paper
• Language: English
• Keywords: agglomeration; core-periphery model; multi-regional; stability; bifurcation
• Subjects: F - International Economics > F2 - International Factor Movements and International Business > F22 - International Migration; F - International Economics > F1 - Trade > F15 - Economic Integration; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies; 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

References

Akamatsu, T., Takayama, Y. and Ikeda, K. (2009) Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models. TUTUP Working Paper, Tohoku University.

Alonso-Villar, O. (2008) A Model of Economic Geography with Demand-Pull and Congestion Costs. Papers in Regional Science, 87: 261-276.

Baldwin, R., Forslid, R., Martin, P., Ottaviano, G. and Robert-Nicoud, 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: 457-465.

Combes, P-P., Mayer, T. and Thisse, J-F. (2008) Economic Geography: The Integration of Regions and Nations. Princeton University Press.

Forslid, R. and Ottaviano, G. (2003) An Analytically Solvable Core -Periphery Model. Journal of Economic Geography, 3: 229-240.

Fudenberg, D. and Levine, D. K. (1998) The Theory of Learning in Games. MIT Press.

Fujita, M. Krugman, P., and Venables, A.J. (1999) The Spatial Economy. MIT Press.

Fujita, M. and Krugman, P. (2004) The new economic geography: Past, present and the future, Papers in Regional Science, 83: 139-164.

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: 109-119.

Gray, R. M. (2006) Toeplitz and Circulant Matrices: A Review, Foundations and Trends in Communications and Information Theory. 2: 155-239.

Helpman, E. (1998) The Size of Regions. in D. Pines, E. Sadka, and Y. Zilcha (eds.), Topics in Public Economics. Theoretical and Applied Analysis, Cambridge: Cambridge University Press, 33-54.

Hirsch, M.W. and Smale, S. (1974) Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press.

Krugman, P. (1991) Increasing Returns and Economic Geography. Journal of Political Economy, 99: 483-499.

Krugman, P. (1993) On the Number and Location of Cities. European Economic Review, 37: 293-298.

Krugman, P. (1996) The Self-Organizing Economy. Blackwell Publishers.

Mossay, P. (2003) Increasing Returns and Heterogeneity in a Spatial Economy. Regional Science and Urban Economics, 33: 419-444.

Murata, Y. (2003) Product Diversity, Taste Heterogeneity, and Geographic Distribution of Economic Activities: Market vs. Non-market Interactions. Journal of Urban Economics, 53: 126-144.

Murata, Y. and Thisse, J.F. (2005) A Simple Model of Economic Geography à la Helpman-Tabuchi. Journal of Urban Economics, 58: 137-155.

Ottaviano, G., Tabuchi, T. and Thisse, J.-F. (2002) Agglomeration and Trade Revisited. International Economic Review, 43: 409-436.

Oyama, D. (2009) Agglomeration under Forward-looking Expectations: Potentials and Global Stability, Regional Science and Urban Economics, 39: 696-713.

Papageorgiou, Y.Y. and Smith, T.R. (1983) Agglomeration as Local Instability of Spatially Uniform Steady-States. Econometrica, 51: 1109-1120.

Picard, P.M. and Tabuchi, T. (2009) Self-Organized Agglomerations and Transport Costs. Economic Theory, 42: 565-589.

Pflüger, M. (2004) A Simple Analytically Solvable, Chamberlinian Agglomeration Model. Regional Science and Urban Economics, 34: 565-573.

Sandholm, W.H. (2009) Population Games and Evolutionary Dynamics. MIT Press.

Tabuchi, T. (1998) Urban Agglomeration and Dispersion: A Synthesis of Alonso and Krugman. Journal of Urban Economics, 44: 333-551.

Tabuchi, T. and Thisse, J.F. (2002) Taste Heterogeneity, Labor Mobility and Economic Geography. Journal of Development Economics, 69: 155-177.

Tabuchi, T., Thisse, J.-F. and Zeng, D.Z. (2005) On the Number and Size of Cities. Journal of Economic Geography, 5: 423-448.

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