A comparative static analysis of urban spatial structure

Abstract

More than a decade has passed since Alonso published his general theory of the urban land market [l]. In the intervening years, a number of other authors have also developed equilibrium models of urban land rent and density [2]. While the structure of these models has been much discussed, there has been virtually no comparative static analysis done on them. The only exception is Mills’ recent numerical analysis of a city with specified functional forms and parameter values [3]. While Mills’ work is excellent in scope, his reliance on Cobb-Douglas functions would seem to limit the generality of his results. The pm-pose of this paper is to conduct a truly general comparative static analysis on two equilibrium models of urban land rent and density. Unlike other authors, we use a utility function whose only requirement is that both goods be “normal” and have positive income effects. This assumption is sufficient to determine the sign of all effects. In both of our spatial systems, the city is viewed as only a small part of a national economy. The production of goods and services occurs at the city center, but wages, prices, and the costs of commuter travel are all exogeneous. Consumers who work in this center earn the same income and have identical preferences. As with Alonso and others, locational choice essentially represents a tradeoff between land and travel. The first of our cities is “closed” in the sense that population size is exogeneous, while consumer levels of welfare must be determined within the system. This situation is typical of industrially advanced societies, where there is essentially no alternative to living in urban areas. In underdeveloped countries, however, rural life often establishes a base-line level of welfare. Migration to cities occurs until urban advantages are reduced. To mirror this process our second city is “open”-the level of utility is take& to be exogeneous and the population size to be endogeneous. In the “closed” model, then, the four parameters are consumer income,