The paper is concerned with the effects of spatial externalities on urban development. With the Herbert-Stevens model of the housing market as the point of departure, equilibrium conditions are formulated. Similar to those of stationary points in quadratic programming, these conditions allow the adaptation of the corresponding algorithms. The nonconvexities caused by the externalities lead to multiple equilibria which may be associated with different city sizes and spatial configurations. The model can be used for the simulation of different empirically observed spatial segregation patterns such as sectors, concentric rings, and multiple nuclei.
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