Linear City Competition with Heterogeneous Product Values

Abstract

We study a model in which a linear city of length 1 exists along the abscissa of a line (0 ≤ x ≤ 1), and consumers are uniformly distributed with density 1 along this interval. There are two firms which sell a kind of goods. Firm 1s goods are valued s1 to the consumers, and firm 2s goods have intrinsic value of s2. A consumer purchase one unit of goods if he chooses to do so. We define two kinds of differentiation. One is the differentiation in the location of each firm. Each firm can locate at a point x. The other differentiation is in the products value to customers. For this differentiation, each firm may try to increase the intrinsic value of its product compared with other firms products. In our model, this differentiation in product value is assumed to be given such that firm 1 offers higher value than firm 2 (s1 > s2). A consumer has to suffer a quadratic transportation cost in addition to the price in order to buy a product from a firm. We first study the duopoly competition of two firms which are located at each extreme end of the linear city. And then we deal with the location problem.