Congestion and the Optimum City Size
Abstract
Many factors interact in subtle and complex ways to determine the size of an urban area. One important factor is transport congestion. Congestion means that the cost in time and comfort of travel to each traveler depends on the density of traffic, that is, on the ratio of the number of travelers to the amount of land used for transportation. In this paper we investigate the effect of congestion on the relation between the optimum size of the city's Central Business District (CBD) and the optimum size of its contiguous suburbs. The model with which this question is investigated has been developed by E. S. Mills and D. M. de Ferranti (M-F), followed by R. M. Solow and W. S. Vickrey. A recent related paper is by Solow. The layout of the model city is circular and it consists of a CBD surrounded by suburbs. The population of the city lives in the suburbs at a given density per unit of land and commutes to the CBD for employment. The density of workers per unit of land in the CBD is also given. Social costs of the urban area are taken to depend on transport costs and on the opportunity costs of land in alternative nonurban use, say, in agriculture. An allocation of land for transport and for housing and a specification of the boundaries of the CBD and the suburbs that minimize social costs are regarded as an optimum, or efficient, urban system. M-F have assumed that the size of the CBD is given and have consequently chosen to neglect the social costs within the CBD. We broaden their analysis to include these costs in order to determine the optimum boundary of the CBD.1 It should be noted that the M-F model is less general than Solow's in that it assumes that the population densities in the suburbs and in the CBD are unaffected by the allocation policy. The neglect of behavioral relations forming the basic structure was found necessary in order to make the problem tractable. Our analysis shows that, within a certain range, the optimum size of the CBD relative to the suburbs depends on the population densities in the CBD and in the suburbs and on the elasticity of congestion costs with respect to traffic density, but is independent of the population size. The analysis may thus be brought to bear upon the very important controversy concerning modern trends in the size of city centers relative to their surrounding suburbs, what is popularly termed the suburbanization process. Some writers, such as B. Chinitz, argue that, as the metropolitan population increases, diminishing returns to scale in the activities inside the CBD may require a decrease in its size relative to the suburbs. Critics have pointed at agglomeration effects, at transport costs, and at the opportunity costs of land as reasons to increase city centers relative to suburbs as the urban population increases. The simple model that underlies our analysis focuses on the congestion aspect alone, neglecting any other considerations. It may thus bring out an important feature of the problem, but it cannot pretend to provide a fully comprehensive analysis.
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