Optimal density of radial major roads in a two-dimensional monocentric city with endogenous residential distribution and housing prices

This paper proposes an analytical urban system equilibrium model for optimizing the density of radial major roads in a two-dimensional monocentric city. The proposed model involves four types of agents: local authorities, property developers, households and household workers (i.e. commuters). The local authorities aim to maximize the total social welfare of the urban system by determining the optimal density of radial major roads in the city. The property developers seek to determine the intensity of their capital investment in the land market to maximize the net profit generated from the housing supply. The households choose residential locations that maximize their utility within a budget constraint, and the commuters choose the radial major roads that minimize their individual costs of travel between home and workplace. A heuristic solution procedure is developed to find the urban system equilibrium solution. A system optimum model is also proposed to optimize the density of radial major roads that maximizes the social welfare of the urban system. The proposed model can endogenously determine household residential distribution and land values across the city, along with the housing market structure in terms of housing prices and space. Numerical comparative static analyses of congestion pricing and road infrastructure investment (adding a new radial major road) are carried out together with evaluation of the effects of the service level of radial major roads, urban population size, and household income level on the urban economy.