How to find marginal revenue from the demand function?
Understand the Problem
The question is asking for the method to calculate marginal revenue from a given demand function. Marginal revenue is the additional revenue that is generated from selling one more unit of a good or service. To find it, we typically need to derive the revenue function from the demand function and then calculate its derivative.
Answer
The marginal revenue is found by calculating the derivative of the revenue function $R(Q) = D(Q) \cdot Q$ with respect to $Q$.
Answer for screen readers
The marginal revenue, calculated as the derivative of the revenue function $R(Q)$ with respect to quantity $Q$, is given by $R'(Q)$.
Steps to Solve
- Identify the demand function
Let's assume the demand function is given as $P = D(Q)$, where $P$ is the price, $D$ is the demand function, and $Q$ is the quantity sold.
- Calculate the revenue function
The revenue function $R(Q)$ can be calculated by multiplying the price $P$ by the quantity $Q$. This gives us: $$ R(Q) = P \cdot Q = D(Q) \cdot Q $$
- Differentiate the revenue function
To find marginal revenue, we need to take the derivative of the revenue function with respect to $Q$. This is represented as: $$ R'(Q) = \frac{dR}{dQ} $$
- Interpret the result
The result from step 3, $R'(Q)$, will provide the marginal revenue, which represents the additional revenue generated from selling one more unit.
The marginal revenue, calculated as the derivative of the revenue function $R(Q)$ with respect to quantity $Q$, is given by $R'(Q)$.
More Information
Marginal revenue is an important concept in economics as it helps businesses determine the optimal level of production. Understanding the relationship between price, quantity sold, and revenue is crucial for effective pricing strategies.
Tips
- Forgetting to multiply the demand function by quantity when calculating the revenue function.
- Not taking the derivative carefully; remember to apply the product rule if necessary.
- Confusing marginal revenue with total revenue; they are distinct concepts!
