Hong Life CalculatorsUnderstanding the marginal revenue calculator — concept and principle
This calculator finds marginal revenue, the extra revenue from each additional unit sold, from two price and quantity points. It shows total revenue at each point, the change in revenue and units, marginal revenue as a share of the new price and, with a marginal cost, the extra profit and whether selling more adds profit. Economics students and pricing managers use it.
How it is calculated
- Total revenue R = price × units
- Marginal revenue MR = (R2 − R1) ÷ (Q2 − Q1)
- MR as % of new price = MR ÷ P2 × 100
- Extra profit = (MR − MC) × (Q2 − Q1)
- Selling the extra units adds profit if MR > MC, reduces it if MR < MC
The principle
When a seller must lower its price to sell more, the lower price applies to all units, not only the extra ones. The revenue gained on the new units is partly offset by the revenue lost on units that would have sold at the higher price. That is why marginal revenue is below the new price for a firm facing a downward-sloping demand curve; on a straight-line demand curve, MR falls twice as fast as the price. Profit rises as long as MR exceeds marginal cost and is highest where MR equals MC. Fixed costs do not enter this comparison.
Worked example
Defaults: 1,000 units at 25; 1,200 units at 23; marginal cost 9.
- R1 = 25 × 1,000 = $25,000; R2 = 23 × 1,200 = $27,600.
- ΔR = $2,600; ΔQ = 200.
- MR = 2,600 ÷ 200 = $13.00, which is 56.5% of the new price of 23.
- Extra profit = (13 − 9) × 200 = $800.
- MR is above MC: Adds profit (MR above MC).
| Second price per unit | Marginal revenue per extra unit |
|---|---|
| 5.75 | -$90.50 |
| 11.5 | -$56.00 |
| 17.2 | -$21.50 |
| 23 | $13.00 |
| 28.8 | $47.50 |
| 34.5 | $82.00 |
| 46 | $151.00 |
How to read the result
Each extra unit sells for 23 but adds only 13 to revenue, because 1,000 units lost 2 each. Since 13 is still above the marginal cost of 9, the price cut pays off. If MR fell below MC, the price cut would lose money even though more units are sold. Repeating the test at further price points shows where MR = MC, the profit-maximising level.
Common mistakes
- Treating the new price as the marginal revenue.
- Comparing MR with average cost instead of marginal cost.
- Using two points where something other than price also changed.
- Ignoring that a price cut may also affect other products you sell.
Frequently asked questions
Why is marginal revenue less than price?
To sell more, the price is lowered on all units, so the revenue gained on the extra units is reduced by the revenue lost on the others.
When is profit maximised?
Where marginal revenue equals marginal cost.
Can marginal revenue be negative?
Yes, when demand is inelastic: a price cut then lowers total revenue.
Sources: OpenStax, Principles of Economics, 3rd ed. (2022), section 9.2 "How a Profit-Maximizing Monopoly Chooses Output and Price"