IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v43y2016i2p257-275.html
   My bibliography  Save this article

Cities’ power laws: the stochastic scaling factor

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0265813515604245
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0265813515604245?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Henderson, J. Vernon, 1986. "Efficiency of resource usage and city size," Journal of Urban Economics, Elsevier, vol. 19(1), pages 47-70, January.
    11. 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.
    12. 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..
    13. 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.
    14. 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.
    15. repec:rre:publsh:v:38:y:2008:i:1:p:29-44 is not listed on IDEAS
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Teulings, Coen N. & Ossokina, Ioulia V. & de Groot, Henri L.F., 2018. "Land use, worker heterogeneity and welfare benefits of public goods," Journal of Urban Economics, Elsevier, vol. 103(C), pages 67-82.
    2. Ricardo Hurtubia & Michel Bierlaire, 2014. "Estimation of Bid Functions for Location Choice and Price Modeling with a Latent Variable Approach," Networks and Spatial Economics, Springer, vol. 14(1), pages 47-65, March.
    3. Zhi Dong & Tien Sing, 2014. "Developer Heterogeneity and Competitive Land Bidding," The Journal of Real Estate Finance and Economics, Springer, vol. 48(3), pages 441-466, April.
    4. Teulings, Coen & Ossokina, Ioulia V. & de Groot, Henri L.F., 2014. "Welfare Benefits of Agglomeration and Worker Heterogeneity," IZA Discussion Papers 8382, Institute of Labor Economics (IZA).
    5. Palmquist, Raymond B., 2006. "Property Value Models," Handbook of Environmental Economics, in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 2, chapter 16, pages 763-819, Elsevier.
    6. De Groot, Henri L.F. & Ossokina, Ioulia V. & Teulings, Coen N, 2014. "Welfare Benefits of Agglomeration and Worker Heterogeneity," CEPR Discussion Papers 10216, C.E.P.R. Discussion Papers.
    7. Tomás Cox & Ricardo Hurtubia, 2021. "Latent Segmentation of Urban Space through Residential Location Choice," Networks and Spatial Economics, Springer, vol. 21(1), pages 199-228, March.
    8. J. Vernon Henderson, 2003. "Urbanization and Economic Development," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 275-341, November.
    9. Huai, Yue & Lo, Hong K. & Ng, Ka Fai, 2021. "Monocentric versus polycentric urban structure: Case study in Hong Kong," Transportation Research Part A: Policy and Practice, Elsevier, vol. 151(C), pages 99-118.
    10. Yannis M. Ioannides & Jeffrey E. Zabel, 2003. "Neighbourhood effects and housing demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(5), pages 563-584.
    11. Ng, Ka Fai & Lo, Hong K., 2017. "On joint railway and housing development: Housing-led versus railway-led schemes," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 464-488.
    12. Gordon H. Hanson, 2000. "Scale Economies and the Geographic Concentration of Industry," NBER Working Papers 8013, National Bureau of Economic Research, Inc.
    13. Thomas J Holmes, 2002. "The Role of Cities: Evidence From the Placement of Sales Offices," Working Papers 02-02, Center for Economic Studies, U.S. Census Bureau.
    14. Chattopadhyay, Sudip, 1998. "An Empirical Investigation into the Performance of Ellickson's Random Bidding Model, with an Application to Air Quality Valuation," Journal of Urban Economics, Elsevier, vol. 43(2), pages 292-314, March.
    15. Cristián Mardones, 2006. "Impacto de la Percepción de la Calidad del Aire sobre el Precio de las Viviendas en Concepción-Talcahuano, Chile," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 43(128), pages 301-330.
    16. Klein, Alexander & Leunig, Tim, 2013. "Gibrat’s Law and the British Industrial Revolution," CAGE Online Working Paper Series 146, Competitive Advantage in the Global Economy (CAGE).
    17. Hirte, Georg & Tscharaktschiew, Stefan, 2018. "The impact of anti-congestion policies and the role of labor-supply margins," CEPIE Working Papers 04/18, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    18. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    19. Sen, Hu & Chunxia, Yang & Xueshuai, Zhu & Zhilai, Zheng & Ya, Cao, 2015. "Distributions of region size and GDP and their relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 46-56.
    20. Alexandra SCHAFFAR, 2012. "La Loi De Zipf Sous Le Prisme De L’Auto-Correlation Spatiale - Les Cas De La Chine Et De L’Inde," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 189-204.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envirb:v:43:y:2016:i:2:p:257-275. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.