How to Calculate Marginal Revenue: Step-by-Step Guide with Examples
The marginal revenue formula is a core concept in microeconomics and commerce, allowing students and businesses to measure the additional revenue earned by selling one more unit of a product. Understanding marginal revenue helps in scoring better in exams, making business decisions, and grasping how firms optimize their production and pricing.
| Type of Revenue | Formula | Use |
|---|---|---|
| Total Revenue (TR) | TR = Price × Quantity Sold | Measures overall sales income |
| Average Revenue (AR) | AR = TR ÷ Quantity | Revenue per unit sold |
| Marginal Revenue (MR) | MR = ΔTR ÷ ΔQ | Extra revenue from selling one more unit |
Marginal Revenue Formula
The marginal revenue formula is MR = ΔTR ÷ ΔQ. Here, MR stands for marginal revenue, ΔTR means change in total revenue, and ΔQ means change in output quantity. Marginal revenue tells you how much extra revenue is earned when one extra unit is sold.
For example, if total revenue increases from ₹500 to ₹550 when sales rise from 10 to 11 units, marginal revenue is (550 - 500) ÷ (11 - 10) = ₹50. This approach makes it easy to learn how to calculate marginal revenue for exams and business scenarios.
How to Calculate Marginal Revenue
To calculate marginal revenue, first find the change in total revenue (ΔTR) between two sales quantities, then divide it by the change in quantity sold (ΔQ). This method helps students answer exam questions accurately and is used in real businesses when planning output levels.
Step-by-Step Calculation
Follow these steps to find marginal revenue from a table of sales:
- Write the total revenue for each sales quantity.
- Calculate the difference in total revenue (ΔTR) between two consecutive quantities.
- Calculate the change in output quantity (ΔQ). Usually, it is 1 unit.
- Apply the formula: MR = ΔTR ÷ ΔQ.
| Units Sold (Q) | Total Revenue (TR) | Marginal Revenue (MR) |
|---|---|---|
| 1 | ₹100 | - |
| 2 | ₹190 | ₹90 |
| 3 | ₹270 | ₹80 |
| 4 | ₹340 | ₹70 |
Marginal Revenue in Different Market Structures
Marginal revenue behaves differently in perfect competition and monopoly. In perfect competition, marginal revenue equals price because firms can sell unlimited units at the market price. In monopoly, marginal revenue is less than price because selling extra units requires lowering the price for all units. This distinction is important for answering conceptual questions and MCQs.
Marginal Revenue and Marginal Cost
Businesses use the marginal revenue formula to compare MR to marginal cost (MC). The profit-maximizing output is where MR = MC. If MR is greater than MC, increasing production adds profit. If MR is less, firms should reduce output. This rule appears frequently in board exams and real-world decision making. Learn more at Marginal Cost Formula.
Solved Example: Marginal Revenue Formula
Let’s solve a typical exam-style marginal revenue question:
- Total revenue when selling 5 units = ₹600
- Total revenue when selling 6 units = ₹650
Apply the formula:
MR = ΔTR ÷ ΔQ
MR = (₹650 - ₹600) ÷ (6 - 5)
MR = ₹50 ÷ 1
MR = ₹50
So, the marginal revenue from the sixth unit is ₹50.
Marginal Revenue Formula Using Calculus
For advanced students, marginal revenue can be calculated using calculus as the derivative of total revenue (TR) with respect to quantity (Q):
This approach is used in higher-level economics and business courses, especially when working with continuous demand functions.
Practice Questions on Marginal Revenue Formula
- Find the marginal revenue if total revenue increases from ₹300 to ₹360 as sales rise from 7 to 8 units.
- Explain the difference between total revenue, average revenue, and marginal revenue using examples.
- In a perfectly competitive market, why does marginal revenue equal price?
- If MR = ₹20 and MC = ₹25, should the firm increase output? Why?
- Given a demand function P = 200 - 5Q, derive the marginal revenue formula using calculus.
Summary Table: Revenue Formulas
| Symbol | Name of Formula | Formula |
|---|---|---|
| TR | Total Revenue | TR = P × Q |
| AR | Average Revenue | AR = TR ÷ Q |
| MR | Marginal Revenue | MR = ΔTR ÷ ΔQ |
Understanding the marginal revenue formula is essential for exams, business analysis, and pricing strategies. At Vedantu, we simplify concepts like marginal revenue and connect them with real-life commerce situations. Use this topic for your last-minute revisions and to build a strong foundation in economics and business studies. For more on related concepts, check our pages on Total Revenue, Average Revenue and Marginal Revenue and Features of Perfect Competition.
FAQs on Marginal Revenue Formula Explained for Commerce Students
1. How do I calculate marginal revenue?
To calculate marginal revenue (MR), find the change in total revenue (TR) when output increases by one unit. The formula is: MR = ΔTR/ΔQ, where ΔTR is the change in total revenue and ΔQ is the change in quantity. For example, if TR increases from $100 to $110 when one more unit is sold, then MR = ($110 - $100)/1 = $10.
2. What is the marginal revenue formula?
The marginal revenue formula is MR = ΔTR/ΔQ. This calculates the additional revenue gained from selling one more unit of a product. ΔTR represents the change in total revenue, and ΔQ represents the change in quantity sold. Understanding this formula is crucial for microeconomics and business decision-making.
3. What does the marginal revenue formula mean?
The marginal revenue formula shows how much extra revenue a firm earns by selling one more unit of its product. It's the change in total revenue divided by the change in quantity. This helps businesses understand the impact of increasing production on their income and make optimal pricing decisions.
4. What is the difference between total revenue and marginal revenue?
Total revenue (TR) is the total income from all sales. Marginal revenue (MR) is the additional revenue from selling just one more unit. For example, if you sell 10 units for $10 each (TR = $100), and selling 11 units brings in $115, then your MR for the 11th unit is $15.
5. Is marginal revenue always equal to price?
No, marginal revenue (MR) equals price only under perfect competition. In other market structures like monopolies, firms must lower prices to sell more, making MR less than the price.
6. How is marginal revenue used in business decisions?
Businesses use marginal revenue (MR) to make key decisions. By comparing MR to marginal cost (MC), they determine the profit-maximizing output level. If MR exceeds MC, increasing production is profitable; if MC exceeds MR, it's not.
7. How is marginal revenue calculated using calculus?
In calculus, marginal revenue (MR) is the derivative of the total revenue (TR) function with respect to quantity (Q): MR = d(TR)/dQ. This provides a more precise way to calculate MR, especially with complex revenue functions.
8. Why does marginal revenue decline as output increases in a monopoly?
In a monopoly, to sell more units, the firm must lower the price of all units. This causes marginal revenue (MR) to fall faster than the price. The decrease in price on all units sold offsets the revenue gain from selling an extra unit.
9. Can marginal revenue ever be negative?
Yes, marginal revenue (MR) can be negative. This happens when decreasing the price to sell more units actually reduces total revenue. This often occurs when demand is highly elastic and price reductions significantly increase quantity demanded.
10. How do you find marginal revenue from a demand function?
To find marginal revenue (MR) from a demand function, first express total revenue (TR) as Price × Quantity. Substitute the demand function for price, then differentiate TR with respect to quantity (Q) to get the MR function: MR = d(TR)/dQ.
11. How is marginal revenue shown on a graph?
In a monopoly, the marginal revenue (MR) curve is a downward-sloping line that lies below the demand (average revenue) curve. In perfect competition, the MR curve is a horizontal line at the market price because firms can sell as much as they want at that price.
12. What is the marginal rate of revenue?
The term "marginal rate of revenue" is not standard economic terminology. It's likely a misunderstanding or variation of marginal revenue, which is the additional revenue from selling one more unit. The correct term to use is marginal revenue.
13. What is marginal revenue equal to?
Marginal revenue (MR) is equal to the change in total revenue (TR) divided by the change in quantity (Q): MR = ΔTR/ΔQ. In perfect competition, MR is equal to the price of the product. In other market structures, MR is typically less than the price.
14. How to find TR and MR?
Total revenue (TR) is calculated by multiplying the price per unit by the quantity sold (TR = P × Q). Marginal revenue (MR) is the change in TR when one more unit is sold (MR = ΔTR/ΔQ). You can find MR from a total revenue table by calculating the change in TR for each additional unit.
