Spatial Oligopolistic Competition
It remains to check that market areas are not disjoint at pi and p;, that is ~c(sz - S1) :;;;;:n:. The third case deals with the remaining zone: c(sz - S1) :;;;; :n: < ~c(sz - S1). Elementary manipulations show that each firm maximizes its profit at the kink of its demand function so that market areas just touch. Accordingly, we have
The preceding discussion leads to the following conclusions. First, when the reservation price is "low enough" compared to the transportation (and/or production) costs, there always exists a price equilibrium. In this case, each firm is a local monopolist in the sense that, at the equilibrium prices, firms do not interact (cross elasticities are zero). In contrast, when the reservation price is "high enough," encroachments on the market areas of neighboring competitors become profitable to the firm, thus making the competitive process more stringent. Not surprisingly, the existence problem now becomes very tricky. An extensive analysis of this important issue is provided in 4.1.