1. What is Marginal Revenue?

Marginal Revenue (MR) is the additional revenue generated by selling one more unit of a good or service. It's calculated as the derivative of the total revenue function with respect to quantity.

2. How Does the Calculator Work?

The calculator uses the marginal revenue formula:

Where:

• \( MR \) — Marginal Revenue (currency per unit)
• \( TR \) — Total Revenue function
• \( Q \) — Quantity of goods sold

Explanation: The calculator numerically computes the derivative of your total revenue function at the specified quantity to determine the marginal revenue.

3. Importance of Marginal Revenue

Details: Marginal revenue is crucial for profit maximization. Businesses use MR to determine optimal production levels, often producing until MR equals marginal cost (MC).

4. Using the Calculator

Tips: Enter your total revenue function in terms of Q (e.g., "50Q - 0.5Q²") and the quantity at which you want to calculate marginal revenue. The calculator will compute the derivative at that point.

5. Frequently Asked Questions (FAQ)

Q1: What if my revenue function is more complex?
A: This calculator handles basic polynomial functions. For more complex functions, you may need specialized mathematical software.

Q2: Can MR be negative?
A: Yes, marginal revenue can be negative when increasing production actually decreases total revenue, often in cases where price decreases significantly with quantity.

Q3: How is MR related to price elasticity?
A: MR = P(1 - 1/|E|), where P is price and E is price elasticity of demand. When |E| > 1, MR > 0.

Q4: What's the difference between MR and AR?
A: MR is marginal revenue (change in total revenue), while AR is average revenue (total revenue divided by quantity).

Q5: When is MR constant?
A: MR is constant in perfectly competitive markets where firms are price takers (TR = P×Q, so MR = P).