For all problems consider a market containing four identical firms, each of which makes an identical product. The inverse demand for this product is P = 100?Q, where P is price and Q is aggregate output. The production costs for firms 1, 2, and 3 are identical and given by C(qi)= 20qi (i= 1,2,3), where qi is the output of firm i. This means that for each of these firms, variable costs are constant at $20 per unit. The production costs for firm 4 are C(q4)= (20+ ?)q4, where ? is some constant. Note that if ? > 0, then firm 4 is a high-cost firm, while if ? < 0, firm 4 is a low-cost firm (|?| < 20). Note also that Q is the total outputs in the market. Assume that if two firms merge, the merged firm will be able to act as an industry leader, making its output decision before the non-merged firms make theirs. Further assume that ? = 0 so that the firms are of equal efficiency.
1) Confirm that a merger between firms 1 and 2 will now be profitable. What has happened to the profits of the non-merged firms and to the product price as a result of this merger?