Aménités urbaines et périurbaines dans une aire métropolitaine de forme fractale

In the THÜNEN tradition, Urban Economy is a striking abstraction, giving models that keep the main features of the wide diversity of real word cities. Nevertheless, this paradigm less suits the modern urban spatial structures (polycentrism, weak centripetal forces, etc.), particularly the peri-urban form of metropolitan areas, which are an urban/rural integrated space. In this paper, we propose a classical micro-economic urban model combined with a « SIERPINSKI?s carpet » geometry, a fractal form which suits for fit together urban and rural areas in a hierarchical structure. Subject to a budget constraint, a household maximises a Cobb-Douglas/CES function, where household?s taste for diversity is modelled with the CES sub-utility functions. Equilibrium is realised on the land market. Household?s optimum depends on the accessibility to hierarchically arranged amenities. Distances between cells are calculated following the metric of the SIERPINSKI?s carpet. An analytical solution is found and simulations show some effects of the fractal geometry. The land rent gradient depends on the accessibility to urban and rural amenities and it is not monotonous in the distance from the CBD, as in Thünen?s models. SIERPINSKI?s form produces results very different from Thünen?s one when commuting cost is low, amenity taste is high or when substituability between amenities is weak. Classification JEL : R14, R21.