Mergers and Antitrust Policy in Related Product Markets: In exercise 26.1, we investigated different ways in which the markets for good xi (produced by firm i) and good xj (produced by firm j) may be related to each other under price competition. We now investigate the incentives for firms to merge into a single firm in such environments—and the level of concern that this might raise among antitrust regulators.
A: One way to think about firms that compete in related markets is to think of the externality they each impose on the other as they set price. For instance, if the two firms produce relatively substitutable goods (as described in (a) below), firm1 provides a positive externality to firm2when it raises p1 because it raises firm2’s demand when it raises its own price.
(a) Suppose that two firms produce goods that are relatively substitutable in the sense that, when the price of one firm’s good goes up, this increases the demand for the other firm’s goods. If these two firms merged, would you expect the resulting monopoly firm to charge higher or lower prices for the goods previously produced by the competing firms? (Think of the externality that is not being taken into account by the two firms as they compete.)
(b) Next, suppose that the two firms produce goods that are relatively complementary in the sense that an increase in the price of one firm’s good decreases the demand for the other firm’s good. How is the externality now different?
(c) When the two firms in (b) merge, would you now expect price to increase or decrease?
(d) If you were an antitrust regulator, which merger would you be worried about: The one in (a) or the one in (b)?
(e) Suppose that instead the firms were producing goods in unrelated markets (with the price of one firm not affecting the demand for the goods produced by the other firm). What would you expect to happen to price if the two firms merge?
(f) Why are the positive externalities we encountered in this exercise good for society?
B: Suppose we have two firms—firm1 and 2—competing on price. The demand for firm i is given by xi (pi, pj) = 1000−10pi + βpj , and each firm faces constant marginal cost c = 20 (and no fixed costs).
(a) Calculate the equilibrium price p∗ as a function of β.
(b) Suppose that the two firms merged into one firm that now maximized overall profit. Derive the prices for the two goods (in terms of β) that the new monopolist will charge — keeping in mind that the monopolist now solves a single optimization problem to set the two prices. (Given the symmetry of the demands, you should of course get that the monopolist will charge the same price for both goods).
(c) Create the following table: Let the first row set different values for β ranging from minus 7.5 to 7.5 in 2.5 increments. Then, derive the equilibrium price (for each β) when the two firms compete and report it in the second row. In a third row, calculate the price charged by the monopoly (that results from the merging of the two firms) for each value of β.
(d) Do your results confirm your intuition from part A of the exercise? If so, how?
(e) Why would firms merge if, as a result, they end up charging a lower price for both goods than they were able to charge individually?
(f) Add two rows to your table —calculating first the profit that the two firms together make in the competitive oligopoly equilibrium and then the profit that the firms make as a monopoly following a merger. Are the results consistent with your answer to (e)?