In a small town with a single cable provider, we can explore the dynamics of a monopoly in the market for cable subscriptions. This scenario illustrates the fundamental economic principles of demand, total revenue, average revenue, and marginal revenue. As the quantity of subscribers increases, the price charged by the provider decreases, demonstrating the law of demand, which states that lower prices typically lead to higher quantities demanded.

Total revenue (TR) is calculated using the formula:

TR = Price × Quantity

For example, if there are 0 subscribers, total revenue is $0. With 1 subscriber paying $70, total revenue becomes $70. Continuing this pattern, we find:

• 2 subscribers at $60 each yield a total revenue of $120.
• 3 subscribers at $50 each yield $150.
• 4 subscribers at $40 each yield $160.
• 5 subscribers at $30 each yield $150.

This shows that total revenue initially increases with the number of subscribers but eventually decreases, indicating a peak point of revenue generation.

Average revenue (AR) is defined as total revenue divided by the quantity of subscribers, which simplifies to the price charged, as shown in the calculations:

AR = TR / Quantity

Thus, average revenue equals price at each level of output, confirming that the average revenue curve aligns with the demand curve.

Marginal revenue (MR), on the other hand, represents the additional revenue generated from selling one more unit (or gaining one more subscriber). It is calculated as:

MR = Change in TR / Change in Quantity

For instance, when moving from 0 to 1 subscriber, the marginal revenue is $70. Adding a second subscriber increases total revenue to $120, resulting in a marginal revenue of $50. Continuing this process, we find:

• From 1 to 2 subscribers: MR = $50
• From 2 to 3 subscribers: MR = $30
• From 3 to 4 subscribers: MR = $10
• From 4 to 5 subscribers: MR = -$10 (indicating a loss in revenue).

This decreasing pattern of marginal revenue highlights a key difference from perfect competition, where marginal revenue equals price. In a monopoly, the downward-sloping demand curve results in marginal revenue being less than average revenue, which has significant implications for profit maximization strategies.

Understanding these concepts is crucial for analyzing how monopolistic firms determine pricing and output levels to maximize profits, particularly as they relate to the intersection of marginal revenue and marginal cost.