The combined equilibrium of travel networks and residential location markets

The combined 'user' equilibrium of travel networks and residential location markets is shown to exist and to be unique in the expected allocation of households to residential locations and to the routes and links of the network, in the vacancies and rents of residential locations and in the congested travel time and cost of each network link. The formulation combines a multinomial logit model of households' location and route choices derived from utility maximization, a binary logit model of house owners' offer decisions derived from profit maximization and the standard model of network congestion. A travel disutility measure (consistent with utility maximization) replaces the standard 'generalized cost function'. The proof utilizes a non-linear programming formulation which reproduces the simultaneous equilibrium conditions of the behavioral formulation. The stability of the unique equilibrium position is briefly discussed, a computational algorithm is proposed and hints for generalized formulations are provided.