To adjust or not to adjust after a cost-push shock? A simple duopoly model with (and without) resilience

We characterize the equilibrium in a homogeneous good Cournot duopoly in which firms have the choice to react to a cost-push shock by paying a lump-sum adjustment cost in order to offset the initial rise in marginal cost. Our results show that the size of the shock and the size of the adjustment cost jointly determine the nature and the number of the equilibria generated in the game. In particular, if the adjustment cost is high enough, at least one firm decides not to adjust at the pure-strategy equilibrium, and such a partial adjustment by the industry can be socially efficient as well. The main conclusions are robust to the endogenization of the adjustment cost as an increasing function of the shock size. Some implications of this partial equilibrium analysis about industry's resilience are outlined.