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Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models

Listed author(s):
  • Akamatsu, Takashi
  • Takayama, Yuki
  • Ikeda, Kiyohiro

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 multi-regional core-periphery (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 multi-regional 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 21738.

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Date of creation: 18 Aug 2009
Date of revision: 25 Dec 2009
Handle: RePEc:pra:mprapa:21738
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  1. Gianmarco Ottaviano & Takatoshi Tabuchi & Jacques-FranÁois Thisse, 2002. "Agglomeration and Trade Revisited," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 409-436, May.
  2. Tabuchi, Takatoshi & Thisse, Jacques-François, 2001. "Taste Heterogeneity, Labour Mobility and Economic Geography," CEPR Discussion Papers 3114, C.E.P.R. Discussion Papers.
  3. Akamatsu, Takashi & Takayama, Yuki, 2009. "A Simplified Approach to Analyzing Multi-regional Core-Periphery Models," MPRA Paper 21739, University Library of Munich, Germany, revised 29 Oct 2009.
  4. Rikard Forslid & Gianmarco I.P. Ottaviano, 2003. "An analytically solvable core-periphery model," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 229-240, July.
  5. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
  6. Tabuchi, Takatoshi, 1998. "Urban Agglomeration and Dispersion: A Synthesis of Alonso and Krugman," Journal of Urban Economics, Elsevier, vol. 44(3), pages 333-351, November.
  7. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
  8. Brakman,Steven & Garretsen,Harry & van Marrewijk,Charles, 2009. "The New Introduction to Geographical Economics," Cambridge Books, Cambridge University Press, number 9780521875325, May.
  9. Ikeda, Kiyohiro & Akamatsu, Takashi & Kono, Tatsuhito, 2012. "Spatial period-doubling agglomeration of a core–periphery model with a system of cities," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 754-778.
  10. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  11. TABUCHI, Takatoshi & THISSE, Jacques-François, "undated". "A new economic geography model of central places," CORE Discussion Papers RP 2267, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. Oyama, Daisuke, 2006. "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," MPRA Paper 15239, University Library of Munich, Germany.
  14. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  15. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-116, March.
  16. Berliant, Marcus & Wang, Ping, 2008. "Urban growth and subcenter formation: A trolley ride from the Staples Center to Disneyland and the Rose Bowl," Journal of Urban Economics, Elsevier, vol. 63(2), pages 679-693, March.
  17. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  18. J. V. Henderson & J. F. Thisse (ed.), 2004. "Handbook of Regional and Urban Economics," Handbook of Regional and Urban Economics, Elsevier, edition 1, volume 4, number 4.
  19. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
  20. Fujita, Masahisa & Mori, Tomoya, 1997. "Structural stability and evolution of urban systems," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 399-442, August.
  21. Murata, Yasusada, 2003. "Product diversity, taste heterogeneity, and geographic distribution of economic activities:: market vs. non-market interactions," Journal of Urban Economics, Elsevier, vol. 53(1), pages 126-144, January.
  22. Fujita, Masahisa & Krugman, Paul & Mori, Tomoya, 1999. "On the evolution of hierarchical urban systems1," European Economic Review, Elsevier, vol. 43(2), pages 209-251, February.
  23. Martin, Philippe & Rogers, Carol Ann, 1994. "Trade Effects of Regional Aid," CEPR Discussion Papers 910, C.E.P.R. Discussion Papers.
  24. Sofia B.S.D. Castro & João Correia-da-Silva & Pascal Mossay, 2012. "The core-periphery model with three regions and more," Papers in Regional Science, Wiley Blackwell, vol. 91(2), pages 401-418, 06.
  25. Anas, Alex, 1983. "Discrete choice theory, information theory and the multinomial logit and gravity models," Transportation Research Part B: Methodological, Elsevier, vol. 17(1), pages 13-23, February.
  26. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  27. Marcus Berliant & Shin-Kun Peng & Ping Wang, 2000. "Production Externalities and Urban Configuration," Vanderbilt University Department of Economics Working Papers 0011, Vanderbilt University Department of Economics.
  28. Fujita, Masahisa, 1988. "A monopolistic competition model of spatial agglomeration : Differentiated product approach," Regional Science and Urban Economics, Elsevier, vol. 18(1), pages 87-124, February.
  29. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
  30. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521772518, May.
  31. Flam, Harry & Helpman, Elhanan, 1987. "Industrial policy under monopolistic competition," Journal of International Economics, Elsevier, vol. 22(1-2), pages 79-102, February.
  32. PICARD, Pierre M. & TABUCHI, Takatoshi, "undated". "Self-organized agglomerations and transport costs," CORE Discussion Papers RP 2182, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  33. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
  34. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
  35. Glaeser, Edward L., 2008. "Cities, Agglomeration, and Spatial Equilibrium," OUP Catalogue, Oxford University Press, number 9780199290444, December.
  36. FUJITA, Masahisa & THISSE, Jacques-François, "undated". "New economic geography: An appraisal on the occasion of Paul Krugman's 2008 Nobel Prize in economic sciences," CORE Discussion Papers RP 2098, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  37. Pascal Mossay, 2003. "Increasing Returns And Heterogeneity In A Spatial Economy," Working Papers. Serie AD 2003-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  38. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-1119, July.
  39. Smith, Tony E., 1976. "Spatial discounting and the gravity hypothesis," Regional Science and Urban Economics, Elsevier, vol. 6(4), pages 331-356, December.
  40. Simon J. Evenett & Wolfgang Keller, 1996. "On Theories Explaining the Success of the Gravity Equation," International Trade 9608001, EconWPA, revised 13 Jun 1997.
  41. B. Curtis Eaton & Myrna Holtz Wooders, 1985. "Sophisticated Entry in a Model of Spatial Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(2), pages 282-297, Summer.
  42. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
  43. Tabuchi, Takatoshi & Thisse, Jacques-François & Zeng, Dao-Zhi, 2002. "On the Number and Size of Cities," CEPR Discussion Papers 3386, C.E.P.R. Discussion Papers.
  44. Bergstrand, Jeffrey H, 1989. "The Generalized Gravity Equation, Monopolistic Competition, and the Factor-Proportions Theory in International Trade," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 143-153, February.
  45. Fujita, Masahisa & Ogawa, Hideaki, 1982. "Multiple equilibria and structural transition of non-monocentric urban configurations," Regional Science and Urban Economics, Elsevier, vol. 12(2), pages 161-196, May.
  46. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  47. BEHRENS, Kristian & THISSE, Jacques-François, "undated". "Regional economics: a new economic geography perspective," CORE Discussion Papers RP 1946, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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