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Exercise 1. Tolls (8 marks) If Lauren drives to work, she has to use two toll roads - B(ertrand) and C(ournot) - named after the two firms which built these two toll ways. Let 7g be the toll charged by firm B for using Bertrand. Similarly, let T'c be the toll charged by firm C for using Cournot. Lauren is willing to pay at most $12 (in tolls) per trip. Her demand for trips per week is given by Q = 12 - TB - Tc Suppose the two firms, B and C, have no other costs. Each firm i(= B, C) chooses T; to maximize its own profit ni = Tie. Part 1 (i) (2 marks) Find TB that maximizes firm B's profit, AB, for a given To. Similarly, find Ic that maximizes firm C's profit for a given TB- (ii) (2 marks) Suppose both firms set toll simultaneously. Let (T;, T) denote the Nash equilibrium prices. Find (Tg, Te) and profits of firms B and C in Nash equilibrium. (iii) (2 marks) Suppose firm B chooses TB first and firm C chooses To afterwards. What toll will firm B choose? (iv) (2 marks) Election is in the corner. Opposition leader, Chandra, is proposing a price cap of $3 on tolls. That is, TA