| Abstract: | A model based on renewal theory generates the number of retail establishments in a place as the outcome of a competitive partitioning process. The available market, measured for example by population or by existing retail sales, is shared among businesses until no market potential market remains. Competing businesses obtain different shares of the market, and the number of establishments is predicted as a discrete random variable. Several alternative formulations are presented of varying generality. One version is successfully tested, using GLIM, on ten business types (SIC two-digit classes) in 232 cities of New York State for 1977 and 1987. The model correctly predicts the form and the variance structure of the relationship between number of establishments and place size. It is shown how the model may be combined with models of city-size distributions to predict aggregate frequency distributions of retail establishments across urban systems. |
