The standard Urban Economics model (Alonso, Muth, Mills) describes analytically an equilibrium of household location in urban areas. We build an agent-based model able to reach this equilibrium in a dynamic way. This allows us to simulate the development of a city by a combination of heterogeneous agents (based on income and preferences for the amenities), transport time cost and amenities locations. We explore the conditions under which non-trivial residential patterns and urban social structure can be obtained.