ABSTRACT
This chapter presents a static model for the equilibrium between supply and demand on an urban housing market. The Disaggregate Residential Equilibrium Assignment Model (DREAM) has two major characteristics: disaggregated representation of both supply and demand, and the role of household income. The housing supply is assumed to be price-elastic in a way that can vary for each location and each housing type. The housing demand is segmented according to the household size, the workplace and the occupation category of the head of the household. In addition, each demand segment presents a statistical distribution of income, treated as a continuous variable (and not a discrete one as is in most applied models). Market equilibrium is characterised first by a set of primal–dual conditions, then by a variational inequality, the continuity of which guarantees the existence of an equilibrium. In the monocentric case, primal–dual conditions are the saddle point conditions of a constrained maximisation programme. Concavity of this programme implies the uniqueness of the equilibrium. We propose a resolution algorithm derived from the assignment of traffic on a transport network. In addition, we present the preliminary results of an application to the Paris region, including the study of a fuel price increase scenario, in order to illustrate the potentialities of the model.
