Suppose Campus Books, a profit-maximizing firm, is the only supplier of the textbook for a given class. The marginal cost of supplying each book is constant and equal to $10, and Campus Books has no fixed costs. The table below shows the reservation prices of the eight students enrolled in the class. $$\begin{array} { | c | c | }
\hline \text { Student } & \begin{array} { c }
\text { Reservation Price } \
\text { (\$/Book) }
\end{array} \
\hline \mathrm { Q } & 60 \
\hline \mathrm { R } & 54 \
\hline \mathrm { S } & 48 \
\hline \mathrm { T } & 42 \
\hline \mathrm { U } & 36 \
\hline \mathrm { V } & 30 \
\hline \mathrm { W } & 24 \
\hline \mathrm { X } & 18 \
\hline
\end{array}$$ How many books will Campus Books sell if it must charge a single price to all of its customers?

Question

Suppose Campus Books, a profit-maximizing firm, is the only supplier of the textbook for a given class. The marginal cost of supplying each book is constant and equal to $10, and Campus Books has no fixed costs. The table below shows the reservation prices of the eight students enrolled in the class. $$\begin{array} { | c | c | } 
\hline \text { Student } & \begin{array} { c } 
\text { Reservation Price } \
\text { (\$/Book) }
\end{array} \
\hline \mathrm { Q } & 60 \
\hline \mathrm { R } & 54 \
\hline \mathrm { S } & 48 \
\hline \mathrm { T } & 42 \
\hline \mathrm { U } & 36 \
\hline \mathrm { V } & 30 \
\hline \mathrm { W } & 24 \
\hline \mathrm { X } & 18 \
\hline
\end{array}$$ How many books will Campus Books sell if it must charge a single price to all of its customers?

Quizplus · Accepted Answer

To maximize profit, Campus Books must charge the highest price that at least one student is willing to pay. Starting from the highest reservation price and moving downward, we can see that the fifth price is 36. Thus if Campus Books charges $36, it can sell books to students U, V, W, and X, giving a total revenue of $144 (4 books sold at $36 apiece). If Campus Books charges $42 or more, it will only sell to student Q, for a total revenue of $60. Thus, $36 is the highest price at which Campus Books can sell books to more than one student, and it will sell 4 books in this case.

Suppose Campus Books, a Profit-Maximizing Firm, Is the Only Supplier