A mass of consumers is uniformly distributed along the interval [0, 1]. Two firms, A and B, are located at points 0 and 1 respectively. We denote by p; the price of firm i E A, B. A consumer located at point r E [0, 1] obtains utility UA(x) = u - PA - tr if he consumes from firm A, and UB(x) = u -PB - t(1 - x) if he consumes from firm B. In the following, we assume that the gross utility u is sufficiently high, so that the market will be covered and all consumers will get positive utility in equilibrium. Both firms have a cost function equal to Ti(qi) = (1+ X)qi, where you should substitute X for the last number of your student ID number. (a) Find the demand function for both firms. [5 marks] (b) Assume firms set their prices simultaneously. Solve for the Nash equilibrium prices, and compute the equilibrium profits. [6 marks] (c) Now, assume a Stackelberg timing, where firm A is the leader. Explain briefly why we should not use the Nash equilibrium concept to solve this game, and solve for the equilibrium prices and profits. [8 marks] (d) Compare the results obtained in parts (b) and (c) and explain the intuition for such difference. Are the equilibria efficient? [5 marks] (e) Suppose that there was a technology that allowed firm A to credibly commit not to change its price (this option to commit would make firm A the Stackelberg leader, as in part c). If only firm A had access to this technology, how much would firm A be willing to pay for it? How would your answer change if the technology was auctioned to the best bidder (between firms A and B)? [4 marks]