5. Professor Kremepuff has published a new textbook. This book will be used in classes for two years, at
which time 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 copies from students 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 in the first year of owning the book for a year is therefore $(p1 − p2/2). In
the first year of publication, the number of students willing to pay $v to own the book for a year is
70,000 − 1,000v. The number of students taking the course in the first year who are willing to pay at
least $w to keep the book for reference rather than resell it is 70,000 − 5,000w. In the second
year, the number of students who have not previously taken the course and are willing to pay at least
$p for a copy of the book is 60,000 − 1,000p. If the publisher sets a price of $p1 in the first year and
$p2 in the second year, with p1 B3 p2, then the total number of copies that the publisher sells over two
years will be equal to
130,000 − 1,000(p1 + p2/2).
140,000 − 1,000(p1 − p2/2).
140,000 − 1,000p1 − 1,000p2.
6. Professor Kremepuff has published a new textbook. This book will be used in classes for two years, at
which time 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 copies from students 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 in the first year of owning the book for a year is therefore $(p1 − p2/2). In
the first year of publication, the number of students willing to pay $v to own the book for a year is
40,000 − 1,000v. The number of students taking the course in the first year who are willing to pay at
least $w to keep the book for reference rather than resell it is 40,000 − 5,000w. In the second year, the
number of students who have not previously taken the course and are willing to pay at least $p for a
copy of the book is 30,000 − 1,000p. If the publisher sets a price of $p1 in the first year and $p2 in the
second year, with p1 B3 p2, then the total number of copies that the publisher sells over two years will
be equal to
80,000 − 1,000(p1 − p2/2).
80,000 − 1,000p1 − 1,000p2.
70,000 − 1,000(p1 + p2/2).
7. A group of 9 consumers are trying to decide whether to connect to a new communications network.
Consumer 1 is of type 1, consumer 2 of type 2, consumer 3 of type 3, and so on. Each consumer’s
willingness to pay to belong to the network is proportional to the number of consumers who belong.
Where k is the number of consumers who belong, the willingness to pay of a type n consumer is equal
to k times n. What is the highest price at which 7 consumers could all connect to the network and
either make a profit or at least break even?