A firm that sells e-books – books in digital form downloadable from the Internet – sells all e-books relating to do-it-yourself topics (home plumbing, gardening, and so on) at the same price. At present, the company can earn a maximum annual profit of $25,000 when it sells 10,000 copies within a year’s time. The firm incurs a 50-cent expense each time a consumer downloads a copy, but the company must spend $100,000 per year developing new editions of the e-books. The company has determined that it would earn zero economic profits if price were equal to average total cost, and in this case it could sell 20,000 copies. Under marginal cost pricing, it could sell 100,000 copies.
In the short run, what is the profit-maximizing price of e-books relating to do-it-yourself topics?
At the profit-maximizing quantity, what is the average total cost of producing e-books?
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To determine the profit-maximizing price of e-books relating to do-it-yourself topics in the short run, we need to compare the marginal cost and the marginal revenue.
1. Marginal Cost (MC): Each copy of the e-book incurs a 50-cent expense, so the marginal cost of producing an additional copy is $0.50.
2. Marginal Revenue (MR): The company can currently sell 10,000 copies per year and earn a maximum profit of $25,000. This implies that the marginal revenue per copy is ($25,000 / 10,000) = $2.50.
To maximize profit, the firm should set the price at the point where marginal cost equals marginal revenue. So, in this case, the profit-maximizing price is $2.50.
Now, let's calculate the average total cost (ATC) at the profit-maximizing quantity.
The profit-maximizing quantity is not given directly, but since the firm can sell 10,000 copies and earn $25,000 profit, we can assume that the average total cost equals the price in this case, as the firm is earning zero economic profits.
Therefore, the average total cost of producing e-books at the profit-maximizing quantity is $2.50.
To find the profit-maximizing price of e-books relating to do-it-yourself topics, we need to analyze the firm's costs, revenues, and profit.
First, let's calculate the revenue per unit. Given that the firm sells all e-books at the same price and sells 10,000 copies with a maximum annual profit of $25,000, we can determine the revenue per unit as follows:
Revenue per unit = Total profit / Number of units sold
= $25,000 / 10,000
= $2.50
Next, we need to consider the costs incurred by the firm. The firm incurs a 50-cent expense each time a consumer downloads a copy, which represents the marginal cost (MC) per unit. Additionally, there is a fixed cost of $100,000 per year for developing new editions of the e-books.
To find the average total cost (ATC) of producing e-books, we need to consider the fixed cost (FC) and variable costs (VC). The variable cost is the sum of the marginal cost per unit (MC) and the expense per download.
Variable cost per unit = MC + Expense per download
= $0.50 (MC) + $0.50 (Expense)
= $1.00
Average total cost per unit = (FC + VC) / Number of units sold
= ($100,000 + ($1.00 x 10,000)) / 10,000
= ($100,000 + $10,000) / 10,000
= $11.00
Now, let's determine the profit-maximizing price and quantity. The firm earns zero economic profits if price equals average total cost and can sell 20,000 copies in this case. Under marginal cost pricing, it could sell 100,000 copies.
To maximize profit in the short run, the firm should set the price equal to marginal cost (MC). This ensures that both the firm and the consumers benefit.
Profit-maximizing price = MC = $0.50
At this price, the firm can sell 100,000 copies (maximum under marginal cost pricing). However, to calculate the profit-maximizing quantity, we need to consider the constraint that the firm can only sell 20,000 copies when the price equals the average total cost (ATC).
Profit-maximizing quantity = Minimum (20,000, 100,000)
= 20,000
Therefore, in the short run, the profit-maximizing price of e-books relating to do-it-yourself topics is $0.50, and the profit-maximizing quantity is 20,000 copies.
At the profit-maximizing quantity of 20,000 copies, the average total cost of producing e-books is $11.00.
1. $10.20
2. $7.70