A book vendor can produce a book at a constant MC equal to zero, and its potential buyers have the following reservation prices: $55, $50, $45, $40, $35, $30, $25, $20, $15, $10, $5. Suppose the book vendor can identify each buyer's reservation price and is able to set an individual price for each buyer. In order to maximize profits, the monopolist will sell:
A)12 books.
B)10 books.
C)11 books.
D)8 books.

Question

Quizplus · Accepted Answer

The monopolist wants to maximize profits. For each book, they will charge a price equal to the buyer's reservation price, and the MC is zero. To maximize profits, the monopolist wants to sell to the buyers with the highest reservation price first, then the next highest, and so on.

In this case, the highest reservation price is $55. The monopolist will sell a book to this buyer for $55, earning a profit of $55. The next highest reservation price is $50. The monopolist will sell a book to this buyer for $50, earning a profit of $50. Continue this process for all reservation prices:

- Sell 1 book to the buyer with reservation price $55 for $55, earning a profit of $55.
- Sell 1 book to the buyer with reservation price $50 for $50, earning a profit of $50.
- Sell 1 book to the buyer with reservation price $45 for $45, earning a profit of $45.
- Sell 1 book to the buyer with reservation price $40 for $40, earning a profit of $40.
- Sell 1 book to the buyer with reservation price $35 for $35, earning a profit of $35.
- Sell 1 book to the buyer with reservation price $30 for $30, earning a profit of $30.
- Sell 1 book to the buyer with reservation price $25 for $25, earning a profit of $25.
- Sell 1 book to the buyer with reservation price $20 for $20, earning a profit of $20.
- Sell 1 book to the buyer with reservation price $15 for $15, earning a profit of $15.
- Sell 1 book to the buyer with reservation price $10 for $10, earning a profit of $10.
- Sell 1 book to the buyer with reservation price $5 for $5, earning a profit of $5.

In total, the monopolist sells 11 books and earns a profit of $320. If the monopolist were to sell to the buyer with the lowest reservation price first, they would only sell 1 book and earn a profit of $5.

A Book Vendor Can Produce a Book at a Constant