The Density Gradients of Small Shops in Cities

Abstract

Changes in the distribution of grocers and greengrocers in Leicester and Northampton are analysed with two regression equations. Change in the density gradient in Leicester is described as a quasi-diffusion process which can be modelled as a quadratic exponential function. In Northampton a monotonic decline in densities is maintained over time, and a first-degree negative exponential equation provides an adequate fit in all years. The difference between the two cities is accounted for by the population required to attract high-order uses which will displace a significant proportion of small shops from the central area and create a ‘density crater’. It may not be possible to define the displacement threshold with any precision.