Suppose that East Frisian Press, discussed in the previous problem, has a constant marginal cost of c = $10 for each copy of Microeconomics for the Muddleheaded that it sells and let the demand functions be
D1(p1 − 0.4p2) = 100 (90 − p1 + 0.4p2)
D2(p2) = 100(90 − p2).
The number of books that people either damage or keep for reference after the first year is
Dk(0.4p2) = 100(90 − 0.8p2).
(This assumption is consistent with the assumption that everyone’s willingness to pay for keeping the book is half as great as her willingness to pay to have the book while she is taking the course.) Assume that East Frisian Press is determined to charge the same price in both years, so that p1 = p2 = p.
(a) If East Frisian Press charges the same price p for Microeconomics for the Muddleheaded in the first and second years, show that the total sales of new copies over the two years are equal to 18, 000 − 180p.
(b) Write an expression for East Frisian’s total revenue, net of variable costs, over the first two years as a function of the price p.
(c) Solve for the price p that maximizes its total revenue net of variable costs over the first two years. ___________ At this price, the net cost to students in the first year of buying the text and reselling it is ___________ The total number of copies sold in the first year will be ___________ The total number of copies that are resold as used books is __________ The total number of copies purchased by students in the second year will be __________. The total number of new copies purchased by students in the second year will be _________ Total revenue net of variable costs over the two years will be ________