Consider a variation of the linear city model of Hotelling

Consider a variation of the linear city model of Hotelling. Buyers are uniformly distributed in a line of length one, where L is the left end and R the right end. Two firms 1,2 compete in prices. Firm 1 is located at distance 1/3 from the left end and firm 2 is located at distance 1/3 from the right end. Since the distance between L and R is 1, this means the distance between firms 1 and 2 is 1/3, as shown in the following diagram. Any buyer purchases one unit of the good from either firm 1 or firm 2. For any buyer, the good has benefit v > 0. To purchase the good from a firm, any buyer has to (i) pay the price set by the firm and (ii) pay the cost of transportation to travel to the firm. The unit transportation cost is 4. Let p1, p2 be the prices set by firms 1,2. (a) [4 points] Consider a buyer b who has distance x from L. Suppose this buyer is on the right of L and left of firm 1, as shown below. In terms of p1, p2, x, determine when this buyer will buy from firm 1 and when it will buy from firm 2. (b) [4 points] Consider a buyer b who has distance x from L. Suppose this buyer is on the right of firm 1, but on the left of firm 2, as shown below. In terms of p1, p2, x, determine when this buyer will buy from firm 1 and when it will buy from firm 2. L (left end) R (right end) distance 1/3 Firm 1 Firm 2 distance 1/3 distance 1/3 L (left end) R (right end) buyer b Firm 1 Firm 2 L (left end) R (right end) Firm 1 buyer b Firm 2   https://www.studyhelpus.com/Questions & Answers/consider-a-variation-of-the-linear-city-model-of-hotelling/