A "linear city" of length 2 lies on the abscissa of a line and consumers are uniformly distributed with density 0.5 along this interval. There are two stores, which sell the same physical good. Two stores are located at the extremes of the city; store 1 is x = 0 and store 2 at x = 2. The unit cost of the good for each store is Consumers incur a transportation cost per unit of length. Thus, a consumer living at x incurs a cost of_tx to go store 1 and a cost of t(2-x) to go to store 2. (Yes, we consider a linear transportation cost function.) Each consumer's surplus (5) from consumption is large enough so that all consumers in this linear city buy one unit from either store 1 or 2. a. Assume that stores choose their prices simultaneously. Find the Nash equilibrium. b. Assume that stores choose their prices sequentially: Store 1 behaves as a first mover and store 2 as a second mover. Find the subgame perfect Nash equilibrium.