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Spatial theory is built on the concept of distance; this distance may be of an economic or ideological form. The foundations of spatial analysis span many disciplines, such as economics, urban studies, and political science. The seminal paper by Ho telling (1929) studied the equilibrium location of two sellers of a homogenous product in a linear town where all consumers are located on a single road. Hotelling’s model is based on physical distance and demonstrates that if the sellers compete only in terms of location (spatial competition) and they are identical in all other dimensions such as quality, costs, and prices, then their optimum location will be the median of the town. Consumers try to minimize travel time when they choose between similar stores. The result is that the stores locate next to each other at the center of the town to capture the most customers. The implicit assumption of spatial models is that people are motivated mainly by self-interest— firms maximize profit and consumers maximize utility.
The notion of space can be extended beyond physical space to include “position” in product characteristics, as described by Lancaster (1979), and “position” in political platforms, as elaborated by Downs (1957). Similarly, in Chamberlain’s (1933) model of monopolistic competition, space is seen as a tool to derive the demand curve faced by the monopolistic firm. Although Hotelling and Smithies (1941) are credited with originating the idea, Downs established spatial theory as a conceptual tool. The modern applications of spatial theory in economics, urban studies, and political science are based on the trade-offs between gains and losses as a result of changes in spatial position. Smithies modified Hotelling’s model by introducing elastic demand so that people at the edges of town might stop shopping at the store if it moved too far to the center. Under perfect inelastic demand conditions, as suggested by Hotelling, consumers are assumed to travel to the center of the town regardless of the opportunity cost of transportation. To introduce a trade-off between the access and transportation cost, Smithies suggested that transportation costs lead to elastic demand at each point on the linear road. Thus, when consumers face an inverse demand function with respect to the distance from the center, they will stop traveling to the center if the cost of travel outweighs the benefit of access. Mills (1972) suggested that allocation of land to differing uses is determined primarily by transportation costs. He argued that variability in transportation costs is a key determinant in the distribution of people across a metropolitan area. The lower transportation costs are, the more decentralized the area is.
Political applications of the spatial model closely followed the spatial theories of economic competition. The electoral models developed by Downs essentially adopt the same principles that economists and social choice theorists use to analyze people’s actions in the marketplace and collective decision making. The economic concept of locational equilibrium has been applied to the political world. Downs assumed that voters were distributed over policy dimensions and that political parties played the role of stores. The tendency of competing businesses toward imitation is applied to political parties during elections. When voters vote for the party closest to them on a single policy dimension, the parties converge to the median voter’s preferences. Since the goal of a political party is to maximize votes, parties and candidates purposefully take positions in the center of the distribution of voter preferences. Restricting issues to a single policy dimension and assuming single-peaked preferences, the expected result is a spatial equilibrium at the position of the median voter (Downs 1957; Black 1958). Since the voters choose to support the candidate nearest to them on the ideological scale, the parties and candidates should adopt platforms that appeal to the median voter to win a majority of the votes. The Downs/Hotelling spatial theory of competition assumes that each voter votes for the candidate from whom he or she derives the highest utility. Downs’s model is an example of the social choice theory; it introduces the electoral trade-off between the number of extremists each party loses by moving toward the center, as compared with the number of moderates it gains. As parties move toward the center of the political spectrum, the voters at the extremes are less likely to identify with mainstream parties and thus choose extremist alternatives or abstention.
Modern monocentric models were developed in the 1960s, largely by Alonso (1964), Muth (1969), and Mills (1972). These models assume the existence of a center in a geographic space to which access is scarce, and therefore valuable. To be close to the center for better access, businesses and consumers bid for land. Land prices are inversely related to distance to the center. Businesses and consumers face a trade-off between land prices and transportation costs. Those who value access to the center more will outbid the others and face higher land prices and lower transportation costs. In Beckmann’s (1973) family choice model, distance to the center is inversely related to the number of dependents in a family unit. Similarly, the smaller size of the ratio of wage earners to family size determines an equilibrium location further from the center. Monocentric models are not concerned with why access is desirable but rather with its consequences, especially the manner in which the market allocates access. However, the need to interact turns out to be sufficient to generate a dense center that exhibits a single peaked-distribution of (homogenous) people across locations. There are many theories of why people want to develop and maintain lasting and positive relations. Beckmann (1976) was the first to focus on the trade-off between the average distance to those with whom one interacts and the amount of the land one consumes. In this model, the city or downtown emerges as a magnet for social relations.
Note that the spatial electoral model (Downs 1957) and the monocentric model (Alonso 1964; Muth 1969; Mills 1972) are also single-peaked as long as the voters are voting on one issue, the city has one center, and the spatial competition has only one dimension. In the real world, however, political discourse and campaign issues seldom fall into a single dimension and goods are different in other dimensions than distance. In this case single-peaked distributions are not possible and multiple equilibria result instead.
Bibliography:
- Alonso, W. 1964. Location and Land Use: Toward a General Theory of Land Rent. Cambridge, MA: Harvard University Press.
- Beckmann, M. J. 1973. Equilibrium Models of Residential Land Use. Regional and Urban Economics 3: 361–368.
- Beckmann, M. J. 1976. Spatial Equilibrium in the Dispersed City. In Mathematical Land Use Theory, ed. Y. Y. Papageorgiou, 117–125. Lexington, MA: Lexington Books.
- Black, D. 1958. The Theory of Committees and Elections. Cambridge, U.K.: Cambridge University Press.
- Chamberlain, E. H. 1933. The Theory of Monopolistic Competition. Cambridge, MA: Harvard University Press.
- Downs, Anthony. 1957. An Economic Theory of Democracy. New York: Harper & Row. Hotelling, H. 1929. Stability in Competition. Economic Journal 39 (1929): 41–57.
- Lancaster, K. 1979. Variety, Equity, and Efficiency. New York: Columbia University Press.
- Mills, E. 1972. Studies in the Structure of the Urban Economy. Baltimore, MD: Johns Hopkins University Press.
- Muth, R. 1969. Cities and Housing: The Spatial Pattern of Urban Residential Land Use. Chicago: University of Chicago Press.
- Smithies, A. 1941. Monopolistic Price Policy in a Spatial Market. Econometrica 9 (1): 63–73.
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