The Conditions for Multi-Center Cities

Abstract

A set of formal conditions for multi-center versus single-center urban forms are derived in this paper, from a mathematical programming model of the spatial arrangement of a city. These conditions indicate that singlecenter arrangements prevail when the marginal costs associated with production, transportation, and residential crowding are small compared to the population and area of the city. The formal conditions are compatible with a class of urban population density functions and this makes it possible to devise a statistical test of the hypothesis of monocentricity. Empirical results for four midwestern cities in 1960 and 1970 indicate that the singlecenter assumption may be untenable. The assumption of a monocentric city structure can greatly simplify the construction of formal models of urban land use patterns, but models which depend on the monocentricity assumption may fail to describe some important features of land use patterns and may conceal important theoretical considerations. The assumption that relevant interactions, especially worktrips, are directed toward a single center generally leads land rent functions, and associated distributions, to assume forms which are continuous, monotonic, and radially symmetric. The simplicity of these forms makes it possible to derive qualitative implications about issues such as the equilibrium distribution of population [1; 4] or the effect of traffic congestion on equilibrium land use patterns [11]. Many of these results would be difficult or impossible to obtain without the single-center assumption. The monocentricity assumption may, however, be untenable in the face of contemporary processes of decentralization which apparently favor the development of dlispersed or multicenter patterns of employment and interaction [101]. The disagreement between the monocentric assumption and observed city forms is especially important in cases where implications drawn from single-center models become invalid or seriously distorted when applied to multi-center cities. The research presented in this paper is an attempt to identify the theoretical and empirical limits of the monocentricity assumption. A general model of the spatial arrangement of urban land uses is presented in which monocentric city forms are a subset of the possible range of solutions. Monocentric solutions are shown to prevail when land use patterns are determined under particular sets of conditions which include conditions on city size, transportation cost, production conditions, and conditions for the consumption of housing. The conditions under which monocentric urban forms can be expected are derived and discussed in an abstract way. It is shown that, in general, monocentric forms prevail when the marginal costs associated with production, transportation, and residential crowding are small compared to the population and area of the city. The class of single-center solutions is also compatible with a class of simple urban population density functions and