Q: A monopolist has TC=2q2+10q+20 and faces demand given by P=58-2q. What is the maximum profit for this monopolist?
A: To maximize profits, the firm should set MR=MC. MC=dTC/dq=4q+10. TR=PQ=(58-2q)*q=58q-2q2. MR=dTR/dq=58-4q. So we have 4q+10=58-4q or 48=8q so qm=6. The price will be 58-2(6)=46, and the profits will be 6*46-2(6)2-10(6)-20=124.