Residential spatial growth with perfect foresight and multiple income groups

Abstract

This paper presents explicit solutions for expanding monocentric cities with two or more income groups. Housing is durable but deteriorates over time, and redevelopment cannot take place. Landlords have perfect foresight. The utility function and housing technology are Cobb-Douglas. Population, per capita income, and transportation costs per mile change at constant percentage rates. The model is solved analytically, using an infinite time horizon. As development proceeds outward, a constant fraction of land is developed with high-income housing, and the remaining land is reserved for future low-income development. At any time, housing is constructed at one distance for high-income consumers, and at a lesser distance for low-income consumers. High-income housing is first occupied by high-income consumers, then filters to low-income consumers, and is ultimately abandoned. Low-income housing is first occupied by low-income households, and ultimately abandoned.