Q: Demand is given by P=240-2Q and TC for each firm is q2. What quantity should each firm produce? How would your answer change if the firms had to pay a fixed cost?
A: For firm 1 TR=(240-2q1-2q2)q1, so MR=240-4q1-2q2. MC is 2q1, so the optimal quantity for firm 1 is 240-4q1-2q2=2q1. By symmetry we know that q1= q2, so 240-4q1-2q1=2q1or 240=8q1or 30=q1and thus 30=q1. If the firms had to pay a fixed cost it would lower their profits, but it would not change MC so it would not change the optimal quantity.