2. Consider a linear city model, in which consumers (normalized to one) are uniformly distributed along the interval [0,1]. There are three firms, located at the points 0.25,0.5, and 0.75. Consumers face quadratic transportation costs; the transportation cost to a consumer of purchasing from a store distance z away is tz2. Each firm has a marginal cost of c. The firms choose prices simultaneously. Assuming full coverage and that all firms sell positive output, find Nash equilibrium prices, and the corresponding quantities and profits. You may assume that in equilibrium the firms at points 0.25 and 0.75 set the same price. 2. Consider a linear city model, in which consumers (normalized to one) are uniformly distributed along the interval [0,1]. There are three firms, located at the points 0.25,0.5, and 0.75. Consumers face quadratic transportation costs; the transportation cost to a consumer of purchasing from a store distance z away is tz2. Each firm has a marginal cost of c. The firms choose prices simultaneously. Assuming full coverage and that all firms sell positive output, find Nash equilibrium prices, and the corresponding quantities and profits. You may assume that in equilibrium the firms at points 0.25 and 0.75 set the same price