Exercise n. 3 Consider a duopoly facing a linear demand P(Q) - A-9, -92 . Each firm produces at the same constant marginal cost, c. Firm /, the leader, chooses its output level first. Firm 2, the follower, chooses its output level after having observed the leader's choice. The market price is then determined by equating aggregate supply with aggregate demand. Suppose that the follower has to pay a per unit tax, f, on every unit it produces and suppose that the tax revenue accrues to the leader. 3.a) Will the leader's output increase or decrease with ?? Explain. 3.b) How would you answer change if the firms payed a simultaneous move game (i.e. Cournot competition)? Exercise n. 4 Consider a market where 5 identical firms operate, producing a homogenous good with a technology represented by the cost function C(q,) =10q, . The inverse demand for the good is given by P(Q) =370-0. 4.a) Find the equilibrium quantities and the profits for each firm if there is Cournot competition. 4.b) Assume that firms / and 2 merge and find the new equilibrium quantities and profits. Is the merger profitable? Why? 4.c) Now suppose that, if firms / and 2 merge, the new firm will be able to act as an industry leader, making its output decision before firms 3 and 4. Firms 3. 4 and 5 will observe the output produced by the merged firm and then simultaneously decide how much to produce. What is the new equilibrium? Would your answer to question b change? Why