PROVIDE APPROPRIATE ANSWERS FOR THE FOLLOWING QUESTIONS PLEASE

Consider n identical firms, which produce a perfectly homogenous good at constant marginal cost c. The market demand is given by p = a - Q, where Q is the total output produced in the industry. The strategic variable of the firm is output, which means this is a Cournot game. a) Find the equilibrium outputs and profits at a pre-merger situation, which is when all the n firms are independent and symmetric! Use nq = Zy=1q; and be careful with its derivation! b) Consider now a merger between m + 1 firms and find the equilibrium output and profit for each independent firm! c) Compare the profits from parts (a) and (b)! Who gains from the merger? d) Show that a merger to monopoly is always profitable for the merging firms! Use n = m + 1!g. (0.5 pt) Following [f.], calculate the post-merger equilibrium profits 7 12 and 5. Then consider that firm 1 merges with firm 3 and competes with firm 2. Answer questions h. (0.5 pt) Write down the best response functions of firm 13 and firm 2 as BR13(42) and BR2(913).c. [0.5 pt] Calculate the equilibrium quantities of. o; and or; 011m: note that :1 = e; so you can apply symmetry on these unto rms and in equi- librium it must be '3': = cg]. d. [0.5 pt] Calculate the equilibrium prots :Ir';I it; and rrg. We next consider rm 1's choice of whom to merge wh. in the absence of any goyemment intervene. Suppose rm I merge with rm 2. So the market competition is between rm 12 and rm 3. Answer questions [f.] to [it-l- e. [0.5 pt] 1Write down the best response functions of rm 12 and rm 3 \"9 Bulll'a] \"\"1 Hashim]- f. [0.5 pt} Following [e.]. calculate the post-merger equilibrium quantity of; and on\". g. [0.5 pt} Following [f.]. calculate the post-merger equilibrium prots TEE and 115