Residential equilibrium in a multifractal metropolitan area

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 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.

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