Textbook authors typically receive a simple percentage of total revenue generated from book sales. The publisher bears all the production costs and chooses the output level. Suppose the retail price of a book is fixed at $50. The author receives $10 per copy, and the firm receives $40 per copy. The firm is interested in maximizing its own profits. Will the author be happy with the book company's output choice? Does the selected output maximize the joint profits (for both the author and company) from the book?
Take a shot, what do you think?
Hint 1: use a monopoly model
Hint 2: no, yes
To determine if the author will be happy with the book company's output choice and if the selected output maximizes the joint profits for both the author and company, we need to calculate the profits for both parties.
Let's start by calculating the profits for the company. We know that the firm receives $40 per copy and the fixed retail price is $50. Therefore, the production cost for each copy is $50 - $40 = $10.
Now, let's calculate the total revenue and total cost for the company based on the output level chosen by the publisher.
Let X be the number of copies sold:
Total Revenue for the company (TR) = Price per copy * Number of copies = $50 * X
Total Cost for the company (TC) = Production cost per copy * Number of copies = $10 * X
The profit for the company (π) can be calculated as:
Profit (π) = Total Revenue - Total Cost = TR - TC = $50X - $10X = $40X
Now, let's calculate the author's profit. We know that the author receives $10 per copy, so the profit for the author can be calculated as:
Author's Profit = Royalty per copy * Number of copies = $10 * X = $10X
To determine if the author will be happy with the book company's output choice, we compare the author's profit with an alternative option. If the author's profit from the chosen output is higher than an alternative option, the author will be happy.
However, before we can compare the author's profit, we should consider that the author's percentage of total revenue is a fixed $10 per copy, regardless of the retail price.
Let's assume the alternative option is for the publisher to sell fewer copies at a higher price, say $60 per copy, while the author's royalty remains the same at $10 per copy.
Total Revenue for the alternative option = Price per copy * Number of copies = $60 * X
Now, the profit for the author with the alternative option can be calculated as:
Author's Profit (alternative option) = Royalty per copy * Number of copies = $10 * X = $10X
Comparing the author's profit with the chosen output ($10X) and the alternative option ($10X), we can see that they are the same. Therefore, the author will be indifferent between the chosen output and the alternative option.
Now, let's consider if the selected output maximizes the joint profits of both the author and the company.
The joint profits (Π) can be calculated as the sum of the company's profit and the author's profit:
Joint Profits (Π) = Company Profit + Author's Profit = $40X + $10X = $50X
Since the joint profits depend on the number of copies sold (X), the selected output level maximizes joint profits as long as X is maximized.
Therefore, if the selected output level maximizes the number of copies sold, it will also maximize the joint profits for both the author and the company. However, this analysis does not consider other factors that may affect the author's satisfaction, such as their expectations or negotiation power with the publisher.