different end of the street, is fixed in location and sells an identical product. Advanced analysis Given the assumptions of the Hotelling model, consumers will choose either firm as long as the combined price and transportation cost of the product is less than the competitive firm. For example, if both firms sell the product at the same price , consumers in quadrants and will pick the firm closest to them. The price realized by the consumer is , where is the price of the product including the cost of transportation. As long as for Firm x is greater than Firm y, consumers will travel to Firm y to purchase their product; this minimizes . Only the consumers who live at point , the halfway point between the two firms, will be indifferent between the two product locations. An example of firm relocation Assumptions Assume that the line in Hotelling’s location model is actually a street with fixed length. All consumers are identical, except they are uniformly located in four quadrants , , , and ; the halfway point between the endpoints is point . Consumers face an equal transportation/time cost for reaching a firm, denoted by ; they have no preferences for the firms. There are two firms in this scenario, Firm x and Firm y; each one is located at a different end of the street, is able to relocate at no cost, and sells an identical product. Analysis In this example, Firm x and Firm y will maximize their profit by increasing their consumer pool. Firm x will move slightly toward Firm y, in order to gain Firm y’s customers. In response, Firm y will move slightly toward Firm x to re-establish its loss, and increase the pool from its competitor. The cycle repeats until both firms are at point , the halfway point of the street where each firm has the same number of customers. This result is known as Hotelling's law, however it was invalidated in 1979 by d'Aspremont, J. Jaskold Gabszewicz and J.-F. Thisse. Consider that quick (short run) price adjustment and slow (long run) location adjustment is modelled as a repeated two-stage game, where in the first stage firms will make an incremental relocation and in the second period, having observed each other's new locations, they will simultaneously chose prices. d'Aspremont et al. (1979) prove that when firms are sufficiently close together (but not