Increasing the Profits of a Subset of Firms in Oligopoly Models with Strategic Substitutes - Gaudet, Gérard; Salant, Stephen W. (American Economic Review, 2016)
Consider an industry composed of N firms in a symmetric equilibrium. Designate a subset of S (< N) firms and marginally reduce the strategic variables of the firms in the subset. If the remaining firms simultaneously make the best reply to this exogenous displacement, under what circumstances will profits of the firms in the designated subset increase? We show that, in the case of Cournot competition among producers of perfect substitutes, a marginal contraction is strictly beneficial (strictly harmful) if and only if the number of firms in the designated subset exceeds the adjusted number of firms outside it by strictly more (strictly less) than one. The adjustment factor is unity when cost and demand functions are linear but, more generally, depends on the convexity of the cost and demand curves. Thus, a marginal contraction of two firms in a triopoly has no effect on the profits of firms in the subset if cost and demand functions are linear; if instead cost is linear but the inverse demand function is strictly concave (strictly convex), a marginal contraction will strictly decrease (strictly increase) profits. The analysis is extended to the effects of nonmarginal exogenous changes in the outputs of the constrained firms. This extension has implications for the relationship of Stackelberg (sequential move) and Nash (simultaneous move) equilibria. Our analysis has broad application. To illustrate, we show that it unifies results in the literature on export subsidies, horizontal mergers, and strikes. The paper is organized as follows. In Section I, our comparative-static result is derived. In Section II, we present a wide range of applications. In the conclusion and the Appendix we generalize our analysis to other situations involving strategic substitutes.