An Aggregative Model of Resource Allocation in a Metropolitan Area
The general ideas that motivate the selection of the model developed below are commonplace in the voluminous recent literature on urban economics and geography. It has frequently been observed that the large size and rapid recent growth of urban areas are responses to income and employment opportunities provided there. It is but a small step from this observation to the assumption that the conditions of production differ in crucial respects as between urban and non-urban areas and as between urban areas of different size. Likewise, it is a common observation on the structure of cities that the nature and intensity of land use vary greatly from city to city and from one part of a city to another. Again, it is but a small step to recognize that a major element of factor substitution is involved in this phenomenon and to analyze models whose production functions will explain the observed factor substitution. Indeed, factor substitution is the most dramatic characteristic of urban structure. For example, the relative price of housing varies somewhat from one part of a city to another, but such variation is small compared with the variation in the relative prices of factors used to produce housing-principally land and structures. It is not unusual for land values to vary by a factor of from ten to one hundred within a distance of ten or twenty miles in a large metropolitan area. And the tremendous variation in capital-land ratios-from skyscrapers and high-rise apartments downtown to single story factories and single family homes on two-acre lots in the suburbs-is the market’s response to these dramatic variations in relative factor prices.