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Emergent Cities: A Microeconomic Explanation for Zipf's Law


  • Robert Axtell and Richard Florida


A model of city formation and evolution is elaborated, based on a multi-agent model of endogenous firm formation. Agents have heterogeneous abilities, are boundedly rational, and interact directly with one another out of equilibrium in team production environments. Each agent works in a firm and each firm has a location. Agents periodically search for positions in other firms that would give them higher utility. Moves between firms are migrations when they involve changes in location. Agents can also start-up new firms if it is welfare-improving to do so. With high probability the location of a new firm is identical with the current location of its founder. However, there is a small chance that a new firm starts up in a different location, with the new location chosen at random. This makes it possible for new cities to occasionally emerge. Over time the movement of individuals across firms combines with the movement of firms across locations to yield clusters of agents and firms in particular locations, i.e., cities. It is demonstrated that under a wide range of conditions these locational clusters reproduce the so-called ÎZipf lawÌ for city sizes, i.e., a Pareto-distribution with exponent 1. This model also yields empirically-significant wage-city size effects, city growth rate distributions, and dependence of city growth rate variance on size. Apparently, this model constitutes the first microeconomic explanation of these phenomena.

Suggested Citation

  • Robert Axtell and Richard Florida, 2001. "Emergent Cities: A Microeconomic Explanation for Zipf's Law," Computing in Economics and Finance 2001 154, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:154

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    Cited by:

    1. Cuberes David, 2009. "A Model of Sequential City Growth," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-41, May.
    2. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    3. Mark Lorenzen & Kristina Vaarst Andersen, 2007. "The Geography of the European Creative Class A Rank-Size Analysis," DRUID Working Papers 07-17, DRUID, Copenhagen Business School, Department of Industrial Economics and Strategy/Aalborg University, Department of Business Studies.
    4. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A complex network approach to urban growth," Environment and Planning A, Pion Ltd, London, vol. 38(10), pages 1941-1964, October.
    5. 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.
    6. repec:wiw:wiwreg:region_4_3_169 is not listed on IDEAS
    7. Gaujal, Bruno & Gulyas, Laszlo & Mansury, Yuri & Thierry, Eric, 2014. "Validating an agent-based model of the Zipf׳s Law: A discrete Markov-chain approach," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 38-49.

    More about this item


    city formation; Zipf's law; agent-based model;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D0 - Microeconomics - - General
    • L0 - Industrial Organization - - General
    • R0 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General


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