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Residential equilibrium in a multifractal metropolitan area



    () (NRA, UMR 1041, CESAER, Dijon, France)


    (CNRS, ThéMA, Université de Franche-Comté, Besançon, France)

  • PEETERS, Dominique

    () (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE) and Department of Geography)

  • THOMAS, Isabelle

    () (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE) and Department of Geography)


A residential location model derived from urban economics is combined with the geometry of a multifractal Sierpinski carpet to represent and model a metropolitan area. This area is made up of a system of built-up patches hierarchically organised around a city centre, and green areas arranged in an inverse hierarchical order (large open-spaces in the periphery). An analytical solution is obtained by using a specific geographic coding system for computing distances. The values of the parameters used in the model are based on the French medium sized metropolitan areas; a realistic benchmark is proposed and comparative-statics simulations are performed. The results show that the French peri-urbanisation process (which took place from 1970 onward) can be explained by an increase in income and a reduction in transport costs. Nevertheless, changes in household preferences, in particular an increased taste for open spaces, can also contribute to urban sprawl by making the gradient of land rents less steep and by making peripheral household locations more desirable

Suggested Citation

  • CAVAILHES, Jean & FRANKHAUSER, Pierre & PEETERS, Dominique & THOMAS, Isabelle, 2009. "Residential equilibrium in a multifractal metropolitan area," CORE Discussion Papers 2009045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2009045

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    References listed on IDEAS

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    Cited by:

    1. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.

    More about this item


    peri-urban; residential localisation; fractal geometry; amenities;

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R21 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Housing Demand

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