How to Calculate Marginal Revenue
Marginal revenue equals the change in total revenue from selling one more unit: MR = ΔTR ÷ ΔQ. In perfect competition MR = price.
The Marginal Revenue formula
Calculator
Enter price and quantity before and after a change and get marginal revenue against the price.
A single-price monopolist has to cut price to sell more; a price taker leaves it unchanged.
Each extra unit adds $5, $4 less than the $9 price, because the lower price applies to every unit sold, not just the extra one.
- Total revenue before
- $40
- Total revenue after
- $45
- MR against price
- MR < price (market power)
How to calculate Marginal Revenue, step by step
- 1Compute total revenue at each quantity. TR = price × quantity, using the price buyers pay at each output level.
- 2Take the change in total revenue. ΔTR between consecutive quantities.
- 3Divide by the change in quantity. MR = ΔTR ÷ ΔQ. For one-unit steps, MR is just the extra revenue from that unit.
Worked example: Marginal Revenue
A monopolist can sell 4 units at $10 (TR = $40) or 5 units at $9 (TR = $45). MR of the 5th unit = 45 − 40 = $5, less than the $9 price, because cutting price to sell the 5th unit sacrifices $1 on each of the first 4.
Why MR falls twice as fast for a price setter
For a firm facing a downward-sloping demand curve, selling one more unit takes cutting the price, and the cut applies to every unit, not only the new one. So marginal revenue is the price of the new unit MINUS the revenue given up on all the units that used to sell for more.
With demand P = 100 − Q, total revenue is 100Q − Q² and marginal revenue is 100 − 2Q. Same intercept, twice the slope. At Q = 10 the price is $90 but marginal revenue is only $80. At Q = 40 the price is $60 and marginal revenue is $20.
That is the whole reason a monopoly graph has two lines where a competitive firm has one, and why the monopolist's price always sits above its marginal revenue.
The point where marginal revenue hits zero
Setting 100 − 2Q = 0 gives Q = 50, and that quantity is worth knowing because three things happen there at once.
Marginal revenue is zero, total revenue is at its maximum of $2,500, and price elasticity of demand is exactly 1. They are the same fact told three ways: revenue stops rising precisely when an extra unit adds nothing, which is precisely where the percentage fall in price cancels the percentage rise in quantity.
It also tells you something a question may ask directly. A profit-maximising firm never produces where marginal revenue is negative, because it could sell less for more money. So the monopolist always operates on the elastic half of its demand curve, to the left of Q = 50 here.
For a perfectly competitive firm none of this applies: price does not change with its output, so marginal revenue equals price and the curve is flat.
Marginal Revenue questions
Why is MR less than price for a monopolist?
To sell another unit, a single-price monopolist must lower the price on all units, so the extra revenue is the new sale minus the revenue lost on every previous unit.
When is marginal revenue negative?
When demand is inelastic: cutting price then lowers total revenue, so the extra unit's MR is negative. A monopolist never produces in this region.
What does the MR curve look like for linear demand?
It shares the demand curve's price-axis intercept but falls twice as steeply, hitting zero at the quantity where total revenue is maximized.
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