Assume a duopoly and let demand be given by P=A-BQ. In addition, let both firms have the same marginal cost c. The interaction between the two firms will be repeated infinitely. Both firms play a grim trigger strategy: they collude and play the cooperative action upon which the firms have agreed (monopoly) as long as both firms always stick to the agreement. However, if any firm should deviate from the agreement then they will revert to the Nash equilibrium forever.
a) if firms collude, what is the profit of each firm?
b) suppose the firms compete in quantities. If firm 1 deviates from collusion in one period, what is the profit of firm 1 in that period? in the subsequent periods?
c) what condition must the discount factor satisfy for collusion to be sustained if the firms compete in quantities?
d) what condition must the discount factor satisfy for collusion toe be sustained if the firms compete in prices?