The demand for Professor Bongmore's new book is given by the function Q = 5,000 - 100p.If the cost of having the book typeset is $9,000, if the marginal cost of printing an extra copy is $4, and if he has no other costs, then he would maximize his profits by
A)not having it typeset and not selling any copies.
B)having it typeset and selling 2,500 copies.
C)having it typeset and selling 4,600 copies.
D)having it typeset and selling 2,300 copies.
E)having it typeset and selling 1,150 copies.

Question

Quizplus · Accepted Answer

To maximize profit, set marginal revenue equal to marginal cost. The demand function is Q = 5,000 - 100p, so the inverse demand function is p = 50 - 0.01Q. Total revenue is TR = pQ = (50 - 0.01Q)Q = 50Q - 0.01Q^2. Marginal revenue is MR = d(TR)/dQ = 50 - 0.02Q. Set MR = MC: 50 - 0.02Q = 4, solving gives Q = 2,300.

The Demand for Professor Bongmore's New Book Is Given by the Function