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Q4. Suppose a duopoly is characterized by the following profits: if the two firms collude and...

Q4. Suppose a duopoly is characterized by the following profits: if the two firms collude and charge the joint profit-maximizing price, they each earn a profit equal to 1500 in each period; if the two firms charge the Cournot–Nash price, they each earn a profit equal to 1200 in each period; and if one firm defects while the other charges the joint profit-maximizing price, the firm that defects earns 3000 and the other earns 0. [20 marks] a) [3 marks] What are each firm’s strategies and the payoff matrix of this game? b) [7 marks] What is the Nash equilibrium? Is this game a prisoner’s dilemma? Explain why or why not. c) [10 marks] Now suppose both firms adopt the following the strategies: (1) Start by cooperating with each firm charging the joint profit-maximizing collusive price; (2) continue to sell at the joint profit-maximizing outputs and price unless the other firm increases its output and lowers its price, in which case produce the Cournot–Nash quantity and charge the Cournot–Nash price forever. What discount rates will sustain collusion

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