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.
Marcus Berliant and Ping Wang
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.
Economic and social activities in different locations interact through systematic connections, which can be modeled as network structures. For example, production processes combine various inputs, tasks, and intermediate products that are spread over space; laborers transmit knowledge and skills along networks of work relations; products are delivered through transportation networks; and local public goods have external effects that spill over into the network of neighborhoods. Such networks bring benefits to connected nodes in the form of externalities. Approaches adopted for modeling networks of locations or that are applicable to spatial economics can be placed into two major categories. First, networks can be formed endogenously when nodes choose links strategically. Thus, networks are outcomes that emerge from strategic equilibria. This approach anylyzes the patterns of networks that are in equilibrium and patterns that are efficient. Second, networks can be a background structure with fixed existing links. In this approach, centrality measures are designed to indicate the importance of a node in the network. In many contexts, these measures determine the equilibrium and efficient behavior of nodes. Networks can be applied to broad issues in urban, regional, and location economics, such as neighborhood interactions, transportation, local public goods, trade, industrial sites, business operations. The strategic connection approach models the network as a strategic game. Both cooperative and noncooperative equilibrium concepts have been adopted in the literature. A link may form cooperatively when both nodes are better off, or one node may force a link noncooperatively onto another. The structure of intracity and intercity networks can be investigated using this framework: In a city, neighborhoods are networks of blocks, which are connected by streets and sidewalks; external benefits spill over into connected blocks; locally integrated neighborhoods emerge in equilibrium; and cities are connected by intercity transportation networks. In such models, the core–periphery patterns of cities are found to emerge in the equilibrium. The structural approach treats network structures as exogenously fixed, and links are not subject to change. In such settings, centrality measures, which indicate how centrally connected the position of a node is in the network, determine the behaviors of nodes. For example, when there are widespread externalities so that payoffs of nodes are determined by efforts of all connected nodes, the equilibrium effort of a node is proportional to its Bonacich centrality measure. Centrality measures determine equilibrium and efficient outcomes in other network settings as well. Examples of such are how conformity in peer networks affects criminal behaviors, how nodes choose security investments against the spread of infection in the network, how intercity transportation networks determine the distribution of city size, and how community residents choose the number of visits to an urban center. Futher findings include, for example, in an economy-wide trade network of intermediate inputs, local economic shocks can cause aggregate production fluctuations; in a network of neighboring jurisdictions, voluntary contributions to local public goods are neutral to income transfers; in a geographical trade network, a firm that already exports to a location will have a higher probability of exporting to a second location if the two locations have a larger volume of trade; and firms spread adverse impacts from a local economic shock through their internal networks across regions.