Quiz 7

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.