Cities in competition, characteristic time, and leapfrogging developers

In a recent paper Czamanski and Roth (2011 Annals of Regional Science 46 101-118) demonstrated that, because the profitability of construction projects is influenced by variations in the time incidence of costs and revenues, despite declining willingness to pay and land gradients with distance from central business districts, profitability can experience local maxima away from urban centers. The time until the realization of revenues was termed 'characteristic time'. Its size is the result of planning polices and can lead to leapfrogging and scattered development, especially when interest rates are low or negligible. We explained this result by modeling the simple behavior of developers in the context of a single linear city. In this paper we consider the case of two municipalities with different development policies and characteristic time functions. We explore local maxima in profitability, typical of disequilibrium situations, especially during periods when cities are growing. Myopic assumptions, in the sense that each city is interested only in what happens on its side of the municipal boundary, can easily lead to unintended leapfrogging. Competition between cities can result in intentional leapfrogging or in spatially concentrated development, depending on the policy objectives. We extend the analysis further and consider qualitatively different cities that give rise to different gravity- type forces and differences in willingness to pay. The demand and supply sides of the building market are integrated into the model. The additional considerations can lead to various patterns of scattered development capable of explaining the spatial structure of metropolitan areas.