Urban spatial development with durable but replaceable capital

Abstract

The theory of urban spatial development, until recently, has been primarily a static theory of economic equilibrium. The models of Alonso [l], Mills [6] and Muth [7] determine a complete spatial equilibrium between the supply and demand for urban land. The study of growth or change in such models, therefore, has been limited exclusively to comparative statics, Wheaton [8]. It should be clear that the central, and in many respects unrealistic assumption of such models, is that housing capital is neither physically nor economically durable. Without durability, there is no opportunity cost to old capital, no barrier to change, and no history to an urban area. Within such a framework, a common set of conclusions emerges, regarding urban spatial structure. Residential density, and the price per unit of land, decline monotonically from the location of employment. A greater population results in higher density at all locations, while increases in income or decreases in the cost of travel create a more steeply sloped density (and price) gradient. In the last few years, there has been a growing awareness that the equilibrium portrayed by such models does not correctly reflect the process of urban development. Theoretical papers by Anas [2, 31 and Brueckner [4], and an empirical model by Harrison and Kain [5] develop an alternative theory of urban spatial development-in which the process of growth is explicitly modeled and in which capital is completely durable. In their models, the spatial development of cities occurs incrementally over time in successive rings from the center of employment outwards. The development of each ring is done with myopic foresight and is therefore determined exclusively by market conditions at the time of development. Once built,