Urban Residential Analysis: 2. Spatial Consumer Equilibrium

Part 1 of this two-part series was concerned with the description and analysis of elements that transcend diverse urban structures of the ‘service’ type. The conclusions were general and abstract. Beyond this unified realm a more detailed description of urban form requires additional assumptions. The nature of such assumptions defines urban form within the confines of positive or normative analysis. Here the additional assumptions define spatial equilibrium within an ‘open’ city. Special cases of such equilibria have been studied extensively. In contrast part 2 develops the general case of a multicentre multiincome city. The properties of spatial-equilibrium bid-rent functions, their synthesis to a composite land-value surface, as well as the properties of this composite, are analyzed in section 1. The next section examines residential land-use patterns generated in a ‘service’ city. Such patterns turn out to be dramatically different from those of other urban types. Section 3 discusses the complex land-value and density surfaces that unfold over the landscape. Finally, section 4 provides what is probably the only analytically solved example of a spatial-equilibrium model related to a hierarchy of centres and to a continuous distribution of incomes over a continuous space.