Understanding Marginal Revenue: Formula, Example & Impact
By Markets & Investing DeskUpdated Nov 10, 2026
Definition
Marginal revenue is the change in total revenue from selling one more unit of a good or service. It measures income only and ignores what that unit costs, so it is not profit.
Key takeaways
- The general formula is MR = ΔTR ÷ ΔQ, the change in total revenue divided by the change in quantity.
- With linear demand P = a − bQ, marginal revenue is MR = a − 2bQ, which has twice the slope of demand.
- A firm maximizes profit at the output where marginal revenue equals marginal cost, then reads price off demand.
- In perfect competition, price, average revenue and marginal revenue are equal at every level of output.
Marginal revenue (MR), sometimes called marginal income, is the change in total revenue that results from selling one more unit of a good or service. If a firm takes in $500 from 50 units and $509 from 51 units, the marginal revenue of the 51st unit is $9. It measures income only and ignores what that extra unit costs to make or sell, so it is not profit.
How marginal revenue works
Total revenue is price times quantity (TR = P × Q). Marginal revenue tracks how that total moves as quantity changes. The key question is whether selling more forces the price down.
A firm that can sell any quantity at the going market price adds exactly that price to revenue with each sale. A firm facing a downward-sloping demand curve must lower the price to sell one more unit, and under a single price the cut applies to every unit sold. The extra unit brings in its price, but the firm gives up some revenue on all the earlier units. Marginal revenue is the net of those two effects:
MR = price of the extra unit − revenue lost on earlier units from the price cut
So marginal revenue for such a firm is below price at every quantity after the first, and it falls as output grows. Eventually the revenue lost on earlier units outweighs the price of the new one, and marginal revenue turns negative.
Marginal revenue is normally measured one unit at a time, but it can also be averaged over a larger block. If revenue rises from $4,000 at 400 units to $4,600 at 500 units, the average marginal revenue across those 100 units is $600 ÷ 100 = $6 per unit, a figure that smooths over any variation inside the block.
The marginal revenue formula
The general formula is:
MR = ΔTR ÷ ΔQ
where ΔTR is the change in total revenue and ΔQ is the change in quantity. With a one-unit step, MR is simply the new total revenue minus the old one.
Finding marginal revenue from a demand function
When demand is written as an equation, marginal revenue is the derivative of total revenue with respect to quantity:
MR = dTR/dQ
Take a linear inverse demand curve, P = a − bQ, where a is the price at which nobody buys and b is the slope.
- Total revenue: TR = P × Q = aQ − bQ²
- Marginal revenue: MR = a − 2bQ
The MR line has the same vertical intercept as demand (a) but twice the slope (2b). The doubling comes from the Q² term in total revenue: every price cut is spread over all units sold. The MR line hits zero at half the quantity where the demand line hits zero. The exact factor of two holds only for straight-line demand. With curved demand, MR still lies below the demand curve, but the gap follows no fixed ratio.
Average revenue
Average revenue is total revenue divided by units sold:
AR = TR ÷ Q
When every unit sells at the same price, AR = (P × Q) ÷ Q = P. The demand curve is therefore also the average revenue curve. When a firm charges different prices for different units, average revenue and price separate. Suppose a shop sells one jacket for $120 and offers a second at half price. The second jacket’s marginal revenue is $60, while average revenue across the two is ($120 + $60) ÷ 2 = $90.
Marginal revenue example
The following hypothetical schedule assumes a firm faces demand of P = 22 − 2Q and charges one price to all buyers.
| Quantity | Price | Total revenue | Marginal revenue |
|---|---|---|---|
| 1 | $20 | $20 | $20 |
| 2 | $18 | $36 | $16 |
| 3 | $16 | $48 | $12 |
| 4 | $14 | $56 | $8 |
| 5 | $12 | $60 | $4 |
| 6 | $10 | $60 | $0 |
| 7 | $8 | $56 | −$4 |
Several patterns appear in the numbers:
- MR is below price after the first unit. The second unit sells for $18 but adds only $16, because the first unit now also sells for $2 less.
- MR falls by $4 per step while price falls by $2. This is the doubled slope in discrete form.
- Total revenue peaks where MR reaches zero. Revenue tops out at $60 between the fifth and sixth units.
- MR turns negative at the seventh unit. The $8 gained on the new sale is smaller than the $12 given up on the first six.
Calculus gives a close but not identical answer: MR = 22 − 4Q gives $14 at Q = 2, while the table shows $16. The table measures the change across the step from 1 to 2 units, which matches the derivative at the midpoint (Q = 1.5).
Marginal revenue and marginal cost
Marginal cost (MC) is the extra cost of producing one more unit. Comparing the two shows whether an extra unit adds to profit:
- MR > MC: the unit adds more revenue than cost, so producing it raises profit.
- MR < MC: the unit costs more than it brings in, so producing it lowers profit.
- MR = MC: the profit-maximizing output, where no further gain is possible.
Continuing the hypothetical example, suppose each unit costs a constant $8 to produce. Units one through three each add more than $8 in revenue, and the fourth adds exactly $8. The fifth adds $4 against an $8 cost, reducing profit by $4, so the firm stops at four units. It then reads the price off the demand curve, not the MR curve: four units sell at $14 each, above marginal cost.
For the same reason, a profit-maximizing firm with positive costs avoids output with negative marginal revenue, where producing more lowers revenue and raises costs at once. A firm might still accept negative MR for reasons outside the model, such as clearing perishable stock or gaining market share.
Marginal revenue under different market structures
Perfect competition
A perfectly competitive firm is a price taker: its output is too small a share of the market to move the price. If that price is $15, every unit adds $15, so P = AR = MR at all levels of output. Its demand, average revenue and marginal revenue curves are the same horizontal line, and setting MR = MC means setting price equal to marginal cost.
Monopoly and imperfect competition
A monopolist, or any firm with a downward-sloping demand curve, has to lower its price to sell more. Its demand curve is its average revenue curve, and its marginal revenue curve lies below it and falls faster. Total revenue rises while MR is positive, peaks where MR is zero and declines once MR is negative. Firms in monopolistic competition and oligopoly face the same pattern to varying degrees.
Elasticity and marginal revenue
Marginal revenue is linked to the price elasticity of demand (e) by the formula:
MR = P × (1 + 1/e)
Here e is negative for normal demand. If demand is elastic (|e| > 1), MR is positive and a price cut raises revenue. At unit elasticity (|e| = 1), MR is zero and revenue is at its maximum. If demand is inelastic (|e| < 1), MR is negative and cutting the price to sell more lowers total revenue. A firm with pricing power and positive marginal cost therefore sets output in the elastic portion of its demand curve.
Distinctions readers often confuse
- Marginal revenue vs. price: They are equal only when the firm can sell more without lowering its price, as in perfect competition.
- Marginal revenue vs. average revenue: AR is revenue per unit across all units sold; MR is the change from the last unit.
- Marginal revenue vs. profit: Marginal profit is MR minus MC. A unit selling for $100 that costs $80 to produce adds $20 of profit. At a $110 cost, the same $100 of marginal revenue brings a $10 loss.
- Marginal revenue and diminishing returns: Falling MR comes from the demand side, from price cuts needed to sell more. Diminishing marginal returns is a production concept: output added by each extra unit of an input such as labor or capital (see factors of production). It pushes marginal cost up; it does not cause MR to fall.
How businesses use marginal revenue
Marginal revenue helps firms decide how much to produce and what to charge, for example whether a discount or volume push will raise total revenue or simply give away margin on sales that would have happened anyway. Comparing revenue at different price and volume levels, from sales history or pricing tests, helps firms estimate how sensitive demand is. Paired with cost data, it points to the output level where the next unit stops paying for itself.
Limitations
- Demand curves are estimated, not observed. Real sales data mix price changes with shifts in demand from seasons, competitors, advertising or the economy, so a revenue change between two periods may not reflect a move along a single demand curve.
- Single-price assumption. The standard results, such as MR below price and the doubled slope, assume one price for all buyers. Discounts, bundles and price discrimination change the calculation.
- Lumpy output. Many products are sold in batches or contracts, so “one more unit” may not be a practical decision.
- Multi-product effects. Selling more of one product can raise or lower sales of another, which a single-product MR figure misses.
FAQs
Can marginal revenue be higher than price?
Not under a single price with downward-sloping demand, where MR is at most equal to price, or in perfect competition, where it equals price. Under perfect price discrimination, each buyer pays their own maximum price, so MR equals the price of the extra unit.
The Bottom Line
Marginal revenue matters to any firm deciding how much to produce or whether a discount will raise revenue. A firm with pricing power gains from extra output only while each unit adds more revenue than it costs, and it avoids output where marginal revenue turns negative. Demand curves are estimated from mixed sales data and the standard results assume a single price, so MR estimates work best when paired with cost data.
