Bertrand oligopoly in a spatial context: The case of quantity independent transportation costs

The theory of spatial competition for a review, see Gabszewicz and Thisse (1985)] is usually based on the assumption of transportation costs which are proportionate to distance and quantity. In reality, however, there exist frequently considerable economies of scale, especially with respect to the conveyed quantity of goods. A good case in point is transportation cost incurred by a consumer patronizing a shopping area. Cost economies of scale will in general influence consumers' optimal choice with respect to quantities and best market places. In the extreme, consumers' outlays on transportation can be considered independent of the purchased quantity, but approximately proportionate to distance. In the present paper, the impact of this assumption on spatial competition is analysed. It will be shown, that existence and uniqueness of spatial oligopolistic equilibrium is restored. Furthermore, due to some residual monopolistic power, prices do not converge to the perfectly competitive equilibrium prices when the distance between the firms shrinks to zero. In conclusion the model exhibits a fundamental difference in the market structure, when the spatial aspect is incorporated.