Selling more units does not always increase total revenue.
Total revenue is price multiplied by quantity in a single-price model. Average revenue is TR/Q and equals that price when all units sell at the same price. Marginal revenue is the change in total revenue from an additional unit. A price-taking firm faces a given price, so an extra unit adds that price to revenue. A firm facing downward-sloping demand may need to lower the common price to sell more, losing some revenue on earlier units; its marginal revenue is then below the new price. Read the given relationships without treating curve derivation as a required skill.
- Total revenue (TR)
- TR is all sales receipts: price x quantity sold when every unit sells at the same price. It is before costs are deducted.
- Average revenue (AR)
- AR is revenue per unit: TR/Q. If every unit sells at the same price, AR equals that price. The AR/demand curve therefore shows the selling price for each quantity.
- Marginal revenue (MR)
- MR is the extra total revenue from increasing sales: change in TR divided by change in Q. If selling more requires a lower price on earlier units too, this lost revenue must be included.
Apply the distinction
Price taker
A price taker accepts the market price rather than choosing it. If an extra sale leaves that price and earlier receipts unchanged, MR = AR = price.
Downward firm demand
A seller facing downward-sloping demand must lower the common price to sell more. That reduces receipts on earlier units, putting MR below price. After choosing output, read its price from AR/demand, not MR.
Linear diagram
For a given continuous linear AR curve, MR has twice its absolute slope. This shortcut is not a general rule for every curve or discrete schedule.
Worked example: A lower price on every batch
The workshop can sell two batches at $28 each or three batches at $26 each. All batches sell at the same chosen price within each option.
- At two batches, TR is $56. At three it is $78, and AR is $26 per batch.
- The third batch adds 78 - 56 = $22 to total revenue. Its selling price is $26, but MR is $22.
- Selling the extra batch brings $26 while reducing receipts on the previous two batches by $2 each: 26 - 4 = 22.
- By contrast, if a small price-taking seller can sell another unit for an unchanged $26 without affecting other receipts, MR is $26.
Watch out for this
An additional unit's selling price must always equal marginal revenue.
Consider whether selling it changes the price received on other units. The equality requires the relevant pricing conditions.
Check your understanding
Two units sell at $10 each; three sell at $9 each, with one common price in each option. What is MR for the third?
- $9.
- $27.
- $7.