Equilibrium commercial activity and travel distributions: Incorporating endogenous prices and travel costs into the Harris-Wilson framework, with some numerical experiments

A classical equilibrium model of shopping travel distribution is revised and extended to include endogenous travel costs and zonal prices of goods sold. At equilibrium, revenues in each zone are equal to the cost of operating retail facilities, which is a function of the level of sales, while zonal trip ends are a function of the prices of goods and costs of travel. It is shown that when diseconomies of scale prevail in retail activity supply, the equilibrium configuration is always unique. Otherwise, a critical relationship between the corresponding parameter and the parameter representing the residents' sensitivity to the price of goods defines a surface in parameter space whose crossing may result in sudden changes in shopping travel demand, from a unique, stable "nonzero" equilibrium, to unstable, multiple "zero" equilibrium, depending on the magnitude of the zonal trip ends. The application of a simple "quasi-balancing factor" algorithm to the identification of the retail activity and travel system equilibrium illustrates the effects of changes in the values of the system's parameters. The results are in general agreement with classical location theory concepts. Several directions for further extension of the model are discussed in the conclusion.