A Disaggregate Residential Equilibrium Assignment Model

This paper presents a set of hypotheses and a mathematical formulation in order to model the equilibrium between supply and demand on an urban housing market. Housing supply is assumed to be price-elastic, in a way that can vary for each location and each dwelling type. Household housing demand is disaggregated on the basis of employment area, category of activity, income and household size. The market equilibrium is characterized by a set of primal-dual conditions, then by a variational inequality whose continuity guarantees the existence of an equilibrium. In the monocentric case, the primal-dual conditions are the saddle point conditions of a constrained maximization program the concavity of which implies the uniqueness of the equilibrium. We propose a resolution algorithm that is derived from traffic assignment on a transportation network. Last, we explore the outcomes of the model in a demonstration application and analyze the sensitivity of the equilibrium to our supply and demand hypotheses.