## General Equilibrium Models

This section concerns general equilibrium models of urban land use, in which the location of households and firms is determined simultaneously. Indeed, overall, the task of such models is to generate structured space from a void space. With that in mind, the assumption of a mono centric city employed in the previous sections is not appropriate here. It has both theoretical and empirical drawbacks. Theoretically, both the spatial organization of land uses and whether a city is monocentric or not should be explained within the framework of the model itself, without assuming any a priori locations. Such a model might well yield a mono centric configuration given a particular parameter set. But it could also yield other

configurations, and herein lies the potential explanatory power. This argument is strengthened by results of empirical work (e.g., Kemper and Schmenner [72], Mills [81], Odland [97] suggesting that the monocentric configuration is but one of many spatial patterns a city can assume. In this section, we hope to show that many types of general equilibrium models of urban land use can be developed and that these models open new perspectives to urban economics. 45

3.1. Prototypes of general equilibrium models A general equilibrium model of urban land use has a trivial solution when it generates no spatial agglomeration and the land use pattern follows a uniform distribution of all activities. Not only are trivial configurations rarely observed, but theoretically, they are not interesting. To construct a meaningful and interesting model, then, with nontrivial solutions, we shall begin by recalling the following result from Starrett [138]. Suppose we have an economy in which the following assumptions are met:

a1. (no relocation cost): All agents are free to choose locations. a2. (homogeneous space): All immobile resources are evenly

distributed over the space, and hence utility functions of households and technology of firms are independent of location.46