For problems 1, 2, 3 and 4 consider a market con- 2. Now assume that each firm incurs fixed costs taining four identical firms each of which makes of F in addition to the variable costs noted an identical product. The inverse demand for above. When two firms merge the merged firm this product is P = 100 - Q, where P is price and has fixed costs of bF where I s b s 2. Q is aggregate output. The production costs for a. Suppose that firms 1 and 2 merge and that firms 1, 2, and 3 are identical and given by C(q) y 2 0. Derive a condition on b, F and y = 20q; (i= 1, 2, 3), where q, is the output of firm for this merger to be profitable. Give an i. This means that for each of these firms, vari- intuitive interpretation of this condition. able costs are constant at $20 per unit. The pro- b. Suppose by contrast that firms 1 and 4 duction costs for firm 4 are C(q,) = (20 + 7)q4, merge. Repeat your analysis in a. where yis some constant. Note that if y> 0, then c. Compare the conditions derived in a. firm 4 is a high-cost firm, while if y