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(b) Consider the Hotelling linear city model. Two firms, 1 and 2, supply a good. The marginal and fixed costs are zero. The firms are located at the extremes of a line of unit length. A continuum of consumers are indexed by x, capturing their preference for a firm, x E [0,1]. Each consumer can demand at most one unit of the good. Their evaluation of the good is 10. The consumers unit transport cost is t 2 0 per unit travelled. Firms compete by setting prices. As a result of the previous assumptions, the utility of consumer x if buying from firm 1 is: U, (x) = 10 - tx - P, and if buying from firm 2 is: Uz(x) = 10 - t(1 - x) - P2- Derive the Nash equilibrium for this game. [7 marks] ii) Assume that in part (a) c = 0. Compare the equilibrium properties (price, market shares, profits) of the two games, and discuss the managerial implications of the findings. [6 marks]