Thus, Q = 3 is the profit maximizing output.

This is not a Pareto efficient equilibrium. Pareto efficiency requires the price to equal marginal cost. Therefore, the Pareto efficient equilibrium would have the price equalling $12 and then from the demand curve we find that the Pareto efficient equilibrium quantity would be the solution to 12 = 24 – 2Q which implies that the Pareto efficient quantity would be Q = 6.

1) Playing “Don’t cooperate” is the dominant strategy for both firms. Note when the other firm plays “Collude”, playing “Collude” yields a payoff of $9 whereas “Don’t cooperate” yields a payoff of $10. Again, when the other firm plays “Don’t cooperate”, playing “Collude” yields a payoff of $7 whereas “Don’t cooperate” yields a payoff of $8. Therefore, playing “Don’t cooperate” yields a higher payoff irrespective of the rival firm’s strategy. Hence, “Don’t cooperate” is a dominant strategy for both firms.

2) The Nash equilibrium strategy profile is {Don’t cooperate, Don’t cooperate}.This is best seen by noticing that since “Don’t cooperate” is a dominant strategy, neither player has a unilateral incentive to deviate from this profile. Hence, it is the unique Nash equilibrium in this game.

3) The Nash equilibrium strategy profile leads to aggregate profits of $16 ($8+$8). The highest aggregate profits are earned in this game from the {Collude, Collude} profile, where both players earn $9 so that the aggregate profits are $18. Therefore, the Nash equilibrium strategy profile does not maximize aggregate profits.

4) The monopolist prices the good at $18 and sells 3 units in equilibrium. Its per unit cost is 12. Thus the monopolist’s total revenue is TR = 3 x 18 = $54 and its total cost is TC = 12 x 3 = 36. Therefore the monopolist’s profit is $54 - $36 = $18.

If the firms successfully collude, their total aggregate profits are equal to the monopolist’s profits. But since they
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