The Profitability of Exogenous Output Contractions

Abstract

We consider a Cournot equilibrium where firms with identical cost functions produce a homogenous good. A subset of these firms faces an exogenously-induced marginal contraction of individual output. We show that for any given finite number of firms greater than one, each firm in the subset will gain (lose) if the number of firms in the subset is sufficiently large (small). With constant marginal costs of production and a linear inverse demand curve, the firms in the subset will gain if and only if they outnumber the firms outside it by more than one. In general, the firms in the subset will gain if and only if their number exceeds by more than one an "adjusted" number of outside firms, where the multiplicative adjustment factor depends on the curvatures of the cost and inverse demand curves. In a price-taking equilibrium, on the other hand, the firms in the subset will never lose from a marginal contraction of their output. Indeed, they will strictly gain if marginal cost is strictly increasing. These local results are used to extend the analysis to the effect on profit of exogenously-induced non-marginal changes in output. These fundamental comparative-static properties have implications for the relationship of Stackelberg and Cournot equilibria. We show how they can be used to generalize some standard duopoly results on first-mover advantage to the case of N-player sequential-move oligopoly games. We also show how these properties of the Cournot model apply directly to the analysis of certain strike situations and underlie the results in the applied literature on gains from export subsidies and on losses from horizontal mergers. Finally, we discuss how the results may be generalized to various assumptions about substitutability and complementarity and to strategic variables other than quantity.