Quiz 6

Q:  A monopolist has costs given by TC=2Q2+8Q+10.  If it faces the market demand of P=88-2Q, what profit will it earn?

A:  To find the optimal quantity we set MR=MC.  MR=88-4Q {this is d/dq of (88-2Q)Q} and MC=4Q+8 {this is d/dq of TC}.
So we have 88-4Q=4Q+8 or 80=8q or q=10.  The price people are willing to pay for 10 units is 68 according to the demand curve.
Thus, TR=68*10=680 and TC=2(10)2+8(10)+10=290 and profit =680-290=390.