Social components of metropolitan population densities

The decline of population density from the center of metropolitan areas can be expressed mathematically as: d _r = d _o e ^gr where d _r is the population density of a subarea at distance r from the center, d _o is the hypothetical density at the center, and g is the population-density gradient, empirically always negative. Expanding this exponential model permits examining systematically the relationship between distance from center and various components of population density—housing-unit density, vacant units, household size, and group-quarters population-and the change over time in these components. For the metropolitan areas of Columbus, Dayton, Hartford, Miami, and Syracuse in 1950 and 1960, housing-unit density decreased from the center more sharply than population density. Vacancies, which increased slightly at the center, were proportionately low in the stable middle zones but somewhat higher in the rapidly growing outer zones. While household size decreased around the center between 1950 and 1960, on the periphery it remained constant or increased slightly because of increased family size. During the same decade, the group-quarters population, relative to total population, shifted outward from the center to the periphery to a small extent.