Quiz 6

Q: Demand is given by P=240-2Q and TC for each firm is q^{2}.
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=(240-2q_{1}-2q_{2})q_{1}, so
MR=240-4q_{1}-2q_{2}. MC is 2q_{1}, so the optimal
quantity for firm 1 is 240-4q_{1}-2q_{2}=2q_{1}.
By symmetry we know that q_{1}= q_{2}, so 240-4q_{1}-2q_{1}=2q_{1}or
240=8q_{1}or 30=q_{1}and thus 30=q_{1}. 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.