Titre: A mean-field model for the spatial distribution of labour, housing and urban air pollution

There exists a relationship between urban air pollution and economic activity: economic activity generates pollution, for instance through heating and transportation ; in turn, pollution spreads around and generates economic disutility. We develop a mean-field model of city coupling a labour market, a housing market, and pollution resulting from automobile commuting. Pollution is modelled through an advection-diffusion equation aiming at representing its physical dispersion.  Agents choose where to work and live in order to maximize their utility, by consuming goods, housing surface and valuing air quality. We prove existence of equilibria, and explore uniqueness when the number of job locations is finite. We provide numerical simulations and we obtain analytical results in the case of a linear monocentric city.

A joint work with Quentin Petit (CEREMADE, Université Paris-Dauphine).