Professor Kremepuff has written a new, highly simplified economics text, Microeconomics for the Muddleheaded, which will be published by East Frisian Press. The first edition of this book will be in print for two years, at which time it will be replaced by a new edition. East Frisian Press has already made all its fixed cost investments in the book and must pay a constant marginal cost of $c for each copy that it sells.
Let p1 be the price charged for new copies sold in the first year of publication and let p2 be the price charged for new copies sold in the second year of publication. The publisher and the students who buy the book are aware that there will be an active market for used copies of Microeconomics for the Muddleheaded one year after publication and that used copies of the first edition will have zero resale value two years after publication. At the end of the first year of publication, students can resell their used textbooks to bookstores for 40% of the second-year price, p2.
The net cost to a student of buying the book in the first year, using it for class, and reselling it at the end of the year is p1 − 0.4p2. The number of copies demanded in the first year of publication is given by a demand function, q1 = D1(p1 − 0.4p2).
Some of the students who use the book in the first year of publication will want to keep their copies for future reference, and some will damage their books so that they cannot be resold. The cost of keeping one’s old copy or of damaging it is the resale price 0.4p2. The number of books that are either damaged or kept for reference is given by a “keepers” demand function, Dk(0.4p2). It follows that the number of used copies available at the end of the first year will be D1(p1 − 0.4p2) − Dk(0.4p2).
Students who buy Microeconomics for the Muddleheaded in the second year of publication will not be able to resell their used copies, since a new edition will then be available. These students can, however, buy either a new copy or a used copy of the book. For simplicity of calculations, let us assume that students are indifferent between buying a new copy or a used copy and that used copies cost the same as new copies in the book store. (The results would be the same if students preferred new to used copies, but bookstores priced used copies so that students were indifferent between buying new and used copies.) The total number of copies, new and used, that are purchased in the second year of publication is q2 = D2(p2).
(a) Write an expression for the number of new copies that East Frisian Press can sell in the second year after publication if it sets prices p1 in year 1 and p2 in year 2.
b) Write an expression for the total number of new copies of Microeconomics for the Muddleheaded that East Frisian can sell over two years at prices p1 and p2 in years 1 and 2.
(c) Would the total number of copies sold over two years increase, decrease, or remain constant if p1 were increased and p2 remained constant?
(d) Write an expression for the total revenue that East Frisian Press will receive over the next two years if it sets prices p1 and p2.
(e) To maximize its total profits over the next two years, East Frisian must maximize the difference between its total revenue and its variable costs. Show that this difference can be written as
(p1 − p2)D1(p1 − 0.4p2) + (p2 − c)t D2(p2) + Dk(0.4p2).
(f) Suppose that East Frisian has decided that it must charge the same price for the first edition in both years that it is sold. Thus it must set p = p1 = p2. Write an expression for East Frisian’s revenue net of variable costs over the next two years as a function of p.