Discrete Choice Theory and the General Equilibrium of Employment, Housing, and Travel Networks in a Lowry-Type Model of the Urban Economy

Abstract

Five influential paradigms established by Beckmann, Lowry, Wilson, Mills, and McFadden are unified by developing a long-run economic general equilibrium model of urban land-use based on probabilistic discrete choice theory. The model takes into account the interdependence of export-oriented and service employment with population. Households' choices of employment type, employment location, type and location of housing, shopping destination, and choice of travel routes in the journey to work and journey to shop are determined simultaneously by means of stochastic utility maximization. Firms' choices of building type and location and landowners' choices of land-use type and density are determined by means of stochastic profit maximization. Travel occurs on a congestible link—node network. The model determines the wage rate for each employment type in each zone, the price of floor space for each building type in each zone, the price of land in each zone, the price of the locally traded composite commodity in each zone, and the peak and off-peak congested travel-cost and travel-time for each link of the network. The quantity of land which remains undeveloped is also determined. I formulate a nonlinear mathematical programming problem which is equivalent to the general equilibrium problem. Using this formulation, I prove the existence and uniqueness of the general equilibrium in all the prices and physical allocations.