the merger of two firms producing complementary products. What is the impact on prices and consumer welfare of a merger that creates a single firm? To be specific, suppose the demand functions for the two products are q1 = a b1 p1 b2 p2 q2 = a b1 p2 b2 p1 and the marginal cost of production is c for each. If b2 > 0, the two products are complements. Note that the model is symmetric, which greatly simplifies the analysis. Scenario A (two separate firms). Firm 1's profit, 1, is given by 1 = (p1 c) q1 = (p1 c) (a b1 p1 b2 p2) Note that profit falls if the other firm increases its price, p2; this is the source of the result we prove below. To find the price that maximizes profit, set the derivative with respect to price equal to zero: 1 p1 = (p1 c) (b1) + (a1 b1 p1 b2 p2) = 0 Firm 2 does the same. Since the model is symmetric, we can skip this step and simply impose the condition p1 = p2. The result is p1 = p2 = a + c b1 2 b1 + b2 (1) It's a little complicated to demonstrate, but this price corresponds to positive quantities only if a > c (b1 + b2) (2) a condition we hereby impose. Scenario B (one firm making both products). The firm's profit is = (p1 c) q1 + (p2 c) q2 = (p1 c) (a b1 p1 b2 p2) + (p2 c) (a b1 p2 b2 p1) We set the derivative with respect to p1 equal to zero: p1 = (p1 c) (b1) + (a b1 p1 b2 p2) + (p2 c) (b2) = 0 By symmetry, p1 = p2, and optimal prices are given by p1 = p2 = a + c b1 + c b2 2 b1 + 2 b2 (3) The price effect of a merger. Under the "positive quantity condition" (2), the price chosen by one single firm, given by (3), is lower than the price chosen by separate firms, 6

given by (1). Therefore, a merger combining the two firms leads to a lower price and leaves the customers of the product better off (that is, consumer surplus is higher). Exercise. Compute prices and profits for Scenarios A and B when a = 12, b1 = 2, b2 = 1, c = 1. How does you answer change if b2 = 2? b2 = 0?