Spatial Competition Amongst Hierarchically Organized Corporations: Prices, Profits, and Shipment Patterns

In recent years, there have been computational and theoretical advances in the analysis both of the equilibrium and of the disequilibrium properties of pricing models in which spatial markets are dominated by autonomous firms engaged in oligopolistic competition. In this paper I develop an approach to the modeling of spatial pricing that transcends the unrealistic institutional simplification that firms are autonomous and independent of corporate organizational structures. Specifically, I hypothesize that competition between corporations takes place at two spatial scales. At the intraurban scale, corporations compete for market share through their franchise sites, where market share is contingent upon the nature and degree of competition between franchises, the spatial structure of the urban market, and the costs of production to the franchise. At the intraurban scale, competition is defined in terms of the strategies of the individual corporations as they adjust their delivered prices to urban markets in response to changes in their costs of production and distribution, the interurban transportation network, and the achieved market share in each urban market. I demonstrate that, for a general corporate objective, there exists at least one spatial price equilibrium and that the stability conditions of this model are identical for two price-setting scenarios: a partial adjustment model and a Bertrand game. For the specific corporate objective of total-profit maximization, I examine the qualitative properties of the hierarchical model.