Fundamental properties of Löschian spatial demand
AbstractSpatial demand is the aggregate demand expressed at a particular location, under given supply conditions, by a set of individual consumers whose locations are dispersed over a geographical market area. Although the concept of spatial demand has played a central role in location and spatial economics since its development by LoÃ«sch and his incorporation of it into his model of spatial competitive equilibrium, a comprehensive rigorous characterization of spatial demand does not presently exist. Accordingly, the contribution of this paper is a quite general formulation of spatial demand and a rigorous specification and evaluation of some of its most important properties. Spatial demand is found to consist of two components: free spatial demand which corresponds to a situation in which the geographic market areas of suppliers do not interact, and competitive spatial demand which corresponds to a situation in which they do. This distinction allows the derivation of conditions for, among other things, the (1)existence of these two components, (2)continuity of the spatial demand function and its first derivative, and (3)convexity or concavity of the spatial demand function. Such properties of spatial demand are basic to an evaluation of the existence, stability, and general nature of spatial competitive equilibrium.