Competitive Delivered Spatial Pricing

This paper contributes to the literature by studying price and production competition between spatially distributed profit maximizing firms. Firms compete by setting delivered prices, planning production, and sending output to each market. Both elastic demand and non-linear production costs are assumed. A non-cooperative game is defined, and its properties are characterized. We find spatial pricing patterns similar to those found by Hoover (1936). Existence and general properties of the Nash price and production equilibrium are shown and sufficient conditions that guarantee the existence of an unique price-production-transportation equilibrium are presented. A convergent algorithm is shown to find the equilibrium and is demonstrated with an example.