Professor Kremepuff's new, user-friendly textbook has just been published.This book will be used in classes for two years, after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year, bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies.)The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication, the number of students willing to pay $v to own a copy of the book for a year is 50,000 - 500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 2,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 30,000 - 500p.If the publisher sets a price of p₁ in the first year and p₂

Question

Professor Kremepuff's new, user-friendly textbook has just been published.This book will be used in classes for two years, after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year, bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies.)The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication, the number of students willing to pay $v to own a copy of the book for a year is 50,000 - 500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 2,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 30,000 - 500p.If the publisher sets a price of p₁ in the first year and p₂ <= p₁ in the second year, then the total number of copies of the book that the publisher sells over the two years will be A)100,000 - 500(p₁ - p₂/2). B)80,000 - 500(p₁ + p₂/2). C)100,000 - 500p₁ - 500p₂. D)100,000 - 1,500p₂. E)80,000 - 750p₂.

Quizplus · Accepted Answer

In the first year, there are 50,000 students willing to pay $v for a new copy of the book, so the publisher will sell 50,000 copies at a price of p₁. In addition, there are 50,000 students willing to pay $w to keep the book for reference, so the publisher will sell an additional 50,000 copies (assuming no overlap with the first group) at a price of p₁. So in total, the publisher will sell 100,000 copies in the first year, for a revenue of 100,000(p₁). In the second year, the publisher will sell some number of new copies (since some students will prefer new to used copies), plus they will also sell some number of used copies that were bought back from bookstores. The number of students taking the course in the second year who are willing to pay $p or more for a new copy is 30,000, so let's assume the publisher sells 30,000 new copies at a price of p₂. The bookstores buy back used copies for p₂/2, so the publisher will receive p₂/2 for each used copy sold. Since there were 100,000 copies sold in the first year, there will be up to 100,000 used copies available for resale in the second year. Assuming all 100,000 used copies are resold in the second year (which is likely an overestimate), the revenue from used copies will be 100,000(p₂/2). So in total over the two years, the publisher's revenue will be: 100,000(p₁) + 30,000(p₂) + 100,000(p₂/2) Simplifying this expression, we get: 80,000(p₁ + p₂/2) So the answer is (B).

Professor Kremepuff's New, User-Friendly Textbook Has Just Been Published