Land is everywhere: the substratum of our existence. In addition, land is intimately linked to the dual concept of location in human activity. Together, land and location are essential ingredients for the lives of individuals as well as for national economies. In the early 21st century, there exist two different approaches to incorporating land and location into a general equilibrium theory. Dating from the classic work of von Thünen (1826), a rich variety of land-location density models have been developed. In a density model, a continuum of agents is distributed over a continuous location space. Given that simple calculus can be used in the analysis, these density models continue to be the “workhorse” of urban economics and location theory. However, the behavioral meaning of each agent occupying an infinitesimal “density of land” has long been in question. Given this situation, a radically new approach, called the σ -field approach, was developed in the mid-1980s for modeling land in a general equilibrium framework. In this approach: (1) the totality of land, L , is specified as a subset of ℝ 2 , (2) all possible land parcels in L are given by the σ -field of Lebesgue measurable subsets of L , and (3) each of a finite number of agents is postulated to choose one such parcel. Starting with Berliant (1985), increasingly more sophisticated σ -field models of land have been developed. Given these two different approaches to modeling land within a general equilibrium framework, several attempts have thus far been proposed for bridging the gap between them. But while a systematic study of the relationship between density models and σ -field models remains to be completed, the clarification of this relationship could open a new horizon toward a general equilibrium theory of land.
Marcus Berliant and Ping Wang
General equilibrium theories of spatial agglomeration are closed models of agent location that explain the formation and growth of cities. There are several types of such theories: conventional Arrow-Debreu competitive equilibrium models and monopolistic competition models, as well as game theoretic models including search and matching setups. Three types of spatial agglomeration forces often come into play: trade, production, and knowledge transmission, under which cities are formed in equilibrium as marketplaces, factory towns, and idea laboratories, respectively. Agglomeration dynamics are linked to urban growth in the long run.