Problems For problems 1, 2, 3, and 4 consider a market must at least be covering their vari- containing four identical firms, each of which able costs. Identify the constraint that makes an identical product. The inverse demand y must satisfy for this to be the case. for this product is P = 100 - Q, where P is b. Assume that firms 1 and 2 merge and price and Q is aggregate output. The production that all firms continue to act as Cournot costs for firms 1, 2, and 3 are identical and given competitors after the merger. Confirm by C(q;) = 20q;; (i = 1, 2, 3), where q; is the that this merger is unprofitable. output of firm i. This means that for each of c. Now assume that firms 1 and 4 merge. these firms, variable costs are constant at $20 Can this merger be profitable if y is per unit. The production costs for firm 4 are positive so that firm 4 is a high-cost C(q4) = (20 + y)q4, where y is some constant. firm? What has happened to the profits Note that if y > 0, then firm 4 is a high-cost of firm 2 as a result of this merger? firm, while if y 0. Derive a condition on b, F, put for each firm, the product price, and and y for this merger to be profitable. the profits of the four firms. For this to Give an intuitive interpretation of this be a "true" equilibrium, all of the firms condition.b. Suppose by contrast that firms 1 and 4 merge. Repeat your analysis in (a). c. Compare the conditions derived in (a) and (b). What does this tell you about mergers that create cost savings? 3. 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 y = 0 so that the firms are of equal efficiency. a. 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? b. Confirm that the two remaining firms will also want to merge and join the leader group given that the leaders act as Cournot competitors with respect to each other (hint: this merger will cre- ate a leader group containing two firms and a follower group containing none). What does this second merger do to the market price