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Explaining the size distribution of cities: X-treme economies

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  • Berliant, Marcus
  • Watanabe, Hiroki

Abstract

The methodology used by theories to explain the size distribution of cities is contrived in that it takes an empirical fact and works backward to first obtain a reduced form of a model, then pushes this reduced form back to assumptions on primitives. The induced assumptions on consumer behavior, particularly about their ability to insure against the city-level productivity shocks in the model, are untenable. With either self insurance or insurance markets, and either an arbitrarily small cost of moving or the assumption that consumers do not perfectly observe the shocks to firms' technologies, the agents will never move. Equilibrium implies a uniform distribution of agents. Even without these frictions, our analysis yields another equilibrium with insurance that gives exactly the same utility level to consumers as the equilibrium studied in the literature, but where consumers never move. Thus, insurance is a substitute for movement. Even aggregate shocks are insufficent to generate consumer movement, since consumers can borrow and save. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5428.

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Date of creation: 24 Oct 2007
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Handle: RePEc:pra:mprapa:5428

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Keywords: Zipf's Law; Gibrat's Law; Size Distribution of Cities; Extreme Value Theory;

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References

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  1. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
  2. Esteban Rossi-Hansberg & Mark L. J. Wright, 2003. "Urban structure and growth," Discussion Paper / Institute for Empirical Macroeconomics 141, Federal Reserve Bank of Minneapolis.
  3. Berliant, Marcus & Kung, Fan-chin, 2009. "Can information asymmetry cause agglomeration?," MPRA Paper 13085, University Library of Munich, Germany.
  4. Duranton, Gilles, 2006. "Some foundations for Zipf's law: Product proliferation and local spillovers," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 542-563, July.
  5. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
  6. Kristian Behrens & Gilles Duranton & Frédéric Robert-Nicoud, 2013. "Productive cities: Sorting, selection, and agglomeration," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 13111, Institut d'Economie et Econométrie, Université de Genève.
  7. Xavier Gabaix, 2009. "The Granular Origins of Aggregate Fluctuations," NBER Working Papers 15286, National Bureau of Economic Research, Inc.
  8. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 41(2), pages 255-258, 09.
  9. 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.
  10. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  11. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378 Elsevier.
  12. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  13. Starrett, David, 1978. "Market allocations of location choice in a model with free mobility," Journal of Economic Theory, Elsevier, vol. 17(1), pages 21-37, February.
  14. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-83, September.
  15. Berliant, Marcus & Kung, Fan-chin, 2010. "Can Information Asymmetry Cause Stratification?," MPRA Paper 21395, University Library of Munich, Germany.
  16. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. On the size of cities
    by Economic Logician in Economic Logic on 2011-09-28 14:08:00
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Cited by:
  1. Duranton, Gilles & Puga, Diego, 2013. "The growth of cities," CEPR Discussion Papers 9590, C.E.P.R. Discussion Papers.
  2. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.
  3. Kim, Ho Yeon, 2012. "Shrinking population and the urban hierarchy," IDE Discussion Papers 360, Institute of Developing Economies, Japan External Trade Organization(JETRO).
  4. Marcus Berliant & Hiroki Watanabe, 2012. "A Scale-Free Transportation Network Explains the City-Size Distribution," ERSA conference papers ersa12p601, European Regional Science Association.
  5. Ho Yeon KIM & Petra de Jong & Jan Rouwendal & Aleid Brouwer, 2012. "Shrinking population and the urban hierarchy
    [Housing preferences and attribute importance among Dutch older adults: a conjoint choice experiment]
    ," ERSA conference papers ersa12p350, European Regional Science Association.
  6. Wen-Tai Hsu & Thomas J. Holmes, 2009. "Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory," 2009 Meeting Papers 342, Society for Economic Dynamics.

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