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Emergent Cities: A Microeconomic Explanation for Zipf's Law

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  • Robert Axtell and Richard Florida

Abstract

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.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 154.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:154

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

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Cited by:
  1. Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
  2. 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.
  3. Claes Andersson & Koen Frenken & Alexander Hellervik, 2005. "A complex network approach to urban growth," Papers in Evolutionary Economic Geography (PEEG) 0505, Utrecht University, Section of Economic Geography, revised Feb 2005.
  4. Cuberes David, 2009. "A Model of Sequential City Growth," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-41, May.
  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. 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.

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