IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0165188912001388
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

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

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

as
in new window

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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  2. Ottaviano, Gianmarco & Thisse, Jacques-François, 1998. "Agglomeration and Trade Revisited," CEPR Discussion Papers 1903, C.E.P.R. Discussion Papers.
  3. Smith, Tony E., 1976. "Spatial discounting and the gravity hypothesis," Regional Science and Urban Economics, Elsevier, vol. 6(4), pages 331-356, December.
  4. 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.
  5. repec:cup:cbooks:9780521698030 is not listed on IDEAS
  6. Simon J. Evenett & Wolfgang Keller, 1998. "On Theories Explaining the Success of the Gravity Equation," NBER Working Papers 6529, National Bureau of Economic Research, Inc.
  7. 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.
  8. Tabuchi, Takatoshi & Thisse, Jacques-François, 2001. "Taste Heterogeneity, Labour Mobility and Economic Geography," CEPR Discussion Papers 3114, C.E.P.R. Discussion Papers.
  9. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar.
  10. 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.
  11. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer, vol. 42(3), pages 565-589, March.
  12. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  13. 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.
  14. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
  15. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  16. Glaeser, Edward L., 2008. "Cities, Agglomeration, and Spatial Equilibrium," OUP Catalogue, Oxford University Press, number 9780199290444, March.
  17. 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.
  18. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
  19. Berliant, Marcus & Wang, Ping, 2007. "Urban growth and subcenter formation: A trolley ride from the Staples Center to Disneyland and the Rose Bowl," MPRA Paper 2770, University Library of Munich, Germany.
  20. Flam, Harry & Helpman, Elhanan, 1987. "Industrial policy under monopolistic competition," Journal of International Economics, Elsevier, vol. 22(1-2), pages 79-102, February.
  21. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
  22. Oyama, Daisuke, 2006. "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," MPRA Paper 15239, University Library of Munich, Germany.
  23. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  24. 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.
  25. 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.
  26. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  27. 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.
  28. 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).
  29. Tabuchi, Takatoshi & Thisse, Jacques-François, 2011. "A new economic geography model of central places," Journal of Urban Economics, Elsevier, vol. 69(2), pages 240-252, March.
  30. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  31. 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.
  32. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  33. 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.
  34. 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.
  35. 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.
  36. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-16, March.
  37. 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.
  38. 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.
  39. repec:cup:cbooks:9780521772518 is not listed on IDEAS
  40. repec:cup:cbooks:9780521875325 is not listed on IDEAS
  41. 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.
  42. 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.
  43. repec:cup:cbooks:9780521775908 is not listed on IDEAS
  44. 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.
  45. 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.
  46. 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.
  47. Martin, Philippe & Rogers, Carol Ann, 1994. "Trade Effects of Regional Aid," CEPR Discussion Papers 910, C.E.P.R. Discussion Papers.
  48. 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.
  49. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:36:y:2012:i:11:p:1729-1759. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.