Optimal Cartel Trigger Price Strategies

This paper describes a dynamic model of industry equilibrium in which a cartel deters deviations from collusive output levels by threatening to produce at Cournot quantities for a period of fixed duration whenever the market price falls below some trigger price. In this model firms can observe only their own production level and a common market price. The market demand curve is assumed to have a stochastic component, so that an unexpectedly low price may signal either deviations from collusive output levels or a "downward" demand shock. This paper characterizes the optimality properties of this model, from the standpoint of the firms which participate in the cartel. In particular, the implications for the equilibrium quantity vector, of setting the trigger price and punishment period length at their optimal values, are assessed. It is demonstrated that, in general, the optimal quantity will exceed that which would maximize expected joint net returns in any single period. The optimal aggregate quantity is shown to be a nondecreasing function of the number of firms, equaling the aggregate Cournot level in the limit, and a nondecreasing function of the variance of the stochastic demand component