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An inverse demand function is a key concept in understanding how prices and quantities are related in economic terms. In simple words, it describes how much consumers are willing to pay for each additional hour of service, like Netflix.

In our example, the inverse demand function is given by:

• \(P = 0.56 - 0.0112 Q\)

Here, \(P\) represents the price per hour, and \(Q\) stands for the quantity in hours. This equation tells us the highest price a consumer is willing to pay based on the time they want to spend streaming.

Overall, an inverse demand function is a useful tool to understand consumer behavior and how price reductions can lead to higher quantities demanded. This formula helps find a balance that can maximize Netflix's profits by targeting the right price point.

Marginal cost is the additional cost incurred in producing one more unit of a product or service. For Netflix, this concept represents the cost of providing an additional hour of streaming to a member.

In this exercise, Netflix's marginal cost is assumed to be zero. Why zero? Because the digital nature of streaming means no tangible goods or additional materials are consumed as more people stream. The infrastructure is already in place, so serving one more viewer doesn't significantly affect costs.

This zero marginal cost allows Netflix to focus on maximizing revenue rather than worrying about increasing costs, making it crucial to leverage pricing strategies effectively to optimize profits.

Revenue maximization involves determining the price and output level that leads to the highest possible revenue for the firm. In the context of Netflix, it means finding the best balance between the number of streaming hours sold and the price charged per hour.

Here's how it's done:

• Use the inverse demand function: \(P = 0.56 - 0.0112 Q\).
• Calculate revenue \(R\) as \(P \times Q\): \(R = (0.56 - 0.0112 Q) \times Q\).
• Derive the expression: \(R = 0.56Q - 0.0112Q^2\).

The aim is to find the quantity \(Q\) that maximizes \(R\), ensuring that Netflix can charge the maximum price that consumers are willing to pay.

To determine the quantity that maximizes revenue, it's essential to use the derivative of the revenue function. This process involves calculus and helps identify the point where increasing or decreasing \(Q\) no longer increases revenue.

In our case:

• Derivative of revenue: \(\frac{dR}{dQ} = 0.56 - 0.0224 Q\).
• Set \(\frac{dR}{dQ} = 0\) to solve for \(Q\).
• Solving gives us: \(Q = 25\).

Substitute this back into the inverse demand function to find the corresponding price. The simplified math reveals \(P = 0.28\), and thus the max profit monthly fee is \(\$7\).

This technique allows Netflix to ensure they're not only attracting more members but also making sure they're earning the most from each subscription.