Comparative Performance of Spatial Models of Economic Markets with Linear Household Demand

Abstract

A fundamental precept of the traditional theory of economic markets holds that price competition among firms within the model of perfect competition maximizes economic welfare.' It follows that the establishment of monopolies or oligopolies will result in reduced economic welfare when compared with a perfectly equilibrium. However, with scattered buyers and positive transportation cost paid by these buyers the demand curve facing each individual firm is necessarily downward sloping, and perfect competition is no longer viable.2 Furthermore, these circumstances in combination with declining average cost warrant the use of spatial models of economic markets. It is the purpose of this paper to examine various spatial models and to compare their impact on economic welfare. Bringing into question the robustness of traditional economic theory, Holahan [11] concludes that in the spatial context a multiplant monopolistic is superior to a competitive equilibrium in high density areas. The spatial model employed by Holahan has been widely accepted as the standard spatial representation of behavior. This model developed by L6sch [13] and further refined by Mills and Lay [14] and Beckmann [1;2] is based on the assumption that in the short run each firm's market area is fixed. The implication of this assumption is that all price changes are undertaken uniformly across all firms within the market. Presumably price changes are undertaken in unison due either to collusion or price leadership. The nature of the L6schian model is evident only in the long run, as free entry is assumed to prevail. Capozza and Van Order [5] have demonstrated that the Loschian model is just one particular type of a class of spatial models compatible with free entry. Each of these