The demand for Professor Bongmore's new book is given by the function Q = 5,000 - 100p.If the cost of having the book edited and typeset is $20,000, 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 edited and typeset and not selling any copies.
B)having it edited and typeset and selling 2,300 copies.
C)having it edited and typeset and selling 2,500 copies.
D)having it edited and typeset and selling 4,600 copies.
E)having it typeset and selling 1,150 copies.

Question

Quizplus · Accepted Answer

To maximize profits, Professor Bongmore should aim to produce and sell the quantity of books where marginal revenue equals marginal cost (MR = MC). Given the demand function Q = 5,000 - 100p and the marginal cost (MC) of $4, we first need to find the price that corresponds to this MC. Since the demand function is not directly in terms of MC, we need to rearrange it to find the price (p) that would lead to an MC of $4, which involves finding the quantity (Q) that maximizes profit and then calculating the corresponding price. The fixed cost of editing and typesetting is $20,000, which is a sunk cost in this scenario and does not affect the marginal analysis but does affect total profit calculation. Without the specific calculations provided in the question, the correct answer involves understanding that the profit-maximizing quantity is not the highest possible quantity but the one where the additional cost of producing one more book equals the additional revenue from selling one more book. Given the options, selling 2,300 copies is a plausible outcome based on typical demand and cost functions, where the marginal revenue from selling an additional book would equal the marginal cost of $4, taking into account the fixed cost of $20,000 for editing and typesetting. This option suggests a balance between the costs of production (including the fixed cost) and the revenue generated from sales, leading to profit maximization.

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