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Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models

  • 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 a 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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 36 (2012)
Issue (Month): 11 ()
Pages: 1729-1759

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Handle: RePEc:eee:dyncon:v:36:y:2012:i:11:p:1729-1759
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
  2. Hofbauer,J. & Sandholm,W.H., 2003. "Evolution in games with randomly disturbed payoffs," Working papers 20, Wisconsin Madison - Social Systems.
  3. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  4. 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).
  5. Flam, Harry & Helpman, Elhanan, 1987. "Industrial policy under monopolistic competition," Journal of International Economics, Elsevier, vol. 22(1-2), pages 79-102, February.
  6. TABUCHI, Takatoshi & THISSE, Jacques-François, . "A new economic geography model of central places," CORE Discussion Papers RP 2267, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  8. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar.
  9. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  10. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
  11. James E. Anderson & Eric van Wincoop, 2000. "Gravity with Gravitas: A Solution to the Border Puzzle," Boston College Working Papers in Economics 485, Boston College Department of Economics.
  12. 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.
  13. repec:att:wimass:9713 is not listed on IDEAS
  14. 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.
  15. Simon J. Evenett & Wolfgang Keller, 1996. "On Theories Explaining the Success of the Gravity Equation," International Trade 9608001, EconWPA, revised 13 Jun 1997.
  16. Ottaviano, Gianmarco & Thisse, Jacques-François, 1998. "Agglomeration and Trade Revisited," CEPR Discussion Papers 1903, C.E.P.R. Discussion Papers.
  17. Smith, Tony E., 1976. "Spatial discounting and the gravity hypothesis," Regional Science and Urban Economics, Elsevier, vol. 6(4), pages 331-356, December.
  18. 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.
  19. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 2002. "Taste heterogeneity, labor mobility and economic geography," Journal of Development Economics, Elsevier, vol. 69(1), pages 155-177, October.
  20. 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 143-53, February.
  21. Behrens, Kristian & Thisse, Jacques-Francois, 2007. "Regional economics: A new economic geography perspective," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 457-465, July.
  22. PICARD, Pierre M. & TABUCHI, Takatoshi, . "Self-organized agglomerations and transport costs," CORE Discussion Papers RP 2182, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521772518.
  24. Berliant, Marcus & Peng, Shin-Kun & Wang, Ping, 2002. "Production Externalities and Urban Configuration," Journal of Economic Theory, Elsevier, vol. 104(2), pages 275-303, June.
  25. 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.
  26. 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.
  27. 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.
  28. Paul Krugman, 1990. "Increasing Returns and Economic Geography," NBER Working Papers 3275, National Bureau of Economic Research, Inc.
  29. Brakman,Steven & Garretsen,Harry & van Marrewijk,Charles, 2009. "The New Introduction to Geographical Economics," Cambridge Books, Cambridge University Press, number 9780521875325.
  30. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  31. Glaeser, Edward L., 2008. "Cities, Agglomeration, and Spatial Equilibrium," OUP Catalogue, Oxford University Press, number 9780199290444.
  32. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-16, March.
  33. Marcus Berliant & Ping Wang, 2005. "Urban Growth and Subcenter Formation: A Trolley Ride from the Staples Center to Disneyland and the Rose Bowl," Urban/Regional 0511012, EconWPA.
  34. Fujita, Masahisa & Thisse, Jacques-François, 2009. "New Economic Geography: An appraisal on the occasion of Paul Krugman's 2008 Nobel Prize in Economic Sciences," Regional Science and Urban Economics, Elsevier, vol. 39(2), pages 109-119, March.
  35. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
  36. 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.
  37. 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.
  38. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-19, July.
  39. 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.
  40. Martin, Philippe & Rogers, Carol Ann, 1994. "Trade Effects of Regional Aid," CEPR Discussion Papers 910, C.E.P.R. Discussion Papers.
  41. 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.
  42. 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.
  43. 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.
  44. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
  45. 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.
  46. 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.
  47. 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.
  48. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
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