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Cities’ power laws: the stochastic scaling factor

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  • Francisco Martínez

Abstract

The power law is a fundamental scaling relationship in the dynamics of organisms and ecological systems. That cities exhibit this law with increasing returns to scale is an empirical finding reported by recent studies. I formulate a microeconomic model of urban systems that supports this evidence assuming a stochastic model, which is based on extreme value theory and random choice to describe all urban agents’ rational stochastic behavior and on Alonso’s urban economic principles. Thus, the observed superlinear increase in rents and wealth emerges, in addition to the classical scale economies, from individuals’ and firms’ behavior due to population diversity and size. A dynamic model of cities’ growth follows, allowing us to predict the expected evolution of urban organizations.

Suggested Citation

  • Francisco Martínez, 2016. "Cities’ power laws: the stochastic scaling factor," Environment and Planning B, , vol. 43(2), pages 257-275, March.
    • Handle: RePEc:sae:envirb:v:43:y:2016:i:2:p:257-275
    DOI: 10.1177/0265813515604245
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    1. Anas, Alex & Hiramatsu, Tomoru, 2012. "The effect of the price of gasoline on the urban economy: From route choice to general equilibrium," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(6), pages 855-873.
    2. L. M.A. Bettencourt & J. Lobo & G. B. West, 2008. "Why are large cities faster? Universal scaling and self-similarity in urban organization and dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 285-293, June.
    3. Alex Anas & Yu Liu, 2007. "A Regional Economy, Land Use, And Transportation Model (Relu‐Tran©): Formulation, Algorithm Design, And Testing," Journal of Regional Science, Wiley Blackwell, vol. 47(3), pages 415-455, August.
    4. Lerman, Steven R. & Kern, Clifford R., 1983. "Hedonic theory, bid rents, and willingness-to-pay: Some extensions of Ellickson's results," Journal of Urban Economics, Elsevier, vol. 13(3), pages 358-363, May.
    5. West, Geoffrey B., 1999. "The origin of universal scaling laws in biology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 104-113.
    6. Ellickson, Bryan, 1981. "An alternative test of the hedonic theory of housing markets," Journal of Urban Economics, Elsevier, vol. 9(1), pages 56-79, January.
    7. Henderson, J. Vernon, 1986. "Efficiency of resource usage and city size," Journal of Urban Economics, Elsevier, vol. 19(1), pages 47-70, January.
    8. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    9. Mattsson, Lars-Göran & Weibull, Jörgen W. & Lindberg, Per Olov, 2014. "Extreme values, invariance and choice probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 81-95.
    10. Geoffrey B. West & James H. Brown & Brian J. Enquist, 2001. "A general model for ontogenetic growth," Nature, Nature, vol. 413(6856), pages 628-631, October.
    11. Duncan Black & Vernon Henderson, 1999. "A Theory of Urban Growth," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 252-284, April.
    12. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1999. "The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms," Working Papers 99-07-047, Santa Fe Institute.
    13. Francisco Martínez & Pedro Donoso, 2010. "The MUSSA II Land Use Auction Equilibrium Model," Advances in Spatial Science, in: Francesca Pagliara & John Preston & David Simmonds (ed.), Residential Location Choice, pages 99-113, Springer.
    14. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    15. Malhotra, Naresh K, 1982. "Information Load and Consumer Decision Making," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 8(4), pages 419-430, March.
    16. repec:rre:publsh:v:38:y:2008:i:1:p:29-44 is not listed on IDEAS
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