Quiz 6

Q: A monopolist has costs given by TC=2Q^{2}+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.