For a price taker, one more unit brings in the price. A monopoly faces the whole downward-sloping demand curve (Monopoly and Barriers to Entry), so to sell one more unit it must lower the price, the same tradeoff behind Elasticity and Total Revenue.
Key idea
For a single-price seller, marginal revenue is less than price (after the first unit): selling one more unit means cutting the price on every unit. With linear demand $P = a - bQ$, marginal revenue is $$MR = a - 2bQ,$$ the same intercept and twice the slope. MR is zero at the middle of the demand line, where demand is unit elastic, and negative below it.
Why it works
Suppose a seller can sell 4 units at \$8 or 5 units at \$7. The 5th unit brings in \$7 (the gain), but the first 4 units now sell for \$1 less each, losing \$4. So $MR = \$7 - \$4 = \$3$, well below the \$7 price. For linear demand, total revenue is $TR = aQ - bQ^2$, and its rate of change is $a - 2bQ$. Where demand is inelastic, cutting the price lowers revenue, so MR is negative there.
| Q | P | TR | MR |
|---|---|---|---|
| 1 | \$10 | \$10 | \$10 |
| 2 | \$9 | \$18 | \$8 |
| 3 | \$8 | \$24 | \$6 |
| 4 | \$7 | \$28 | \$4 |
| 5 | \$6 | \$30 | \$2 |
| 6 | \$5 | \$30 | \$0 |
Worked example: From a demand schedule
Using the table, find the marginal revenue of the 4th unit and explain why it is less than \$7.
- $TR(4) = \$28$ and $TR(3) = \$24$, so $MR = \$4$.
- The 4th unit sells for \$7 (gain), but the first 3 units drop from \$8 to \$7, losing $3 \times \$1 = \$3$.
- $\$7 - \$3 = \$4$.
Answer: \$4.
Worked example: From a linear demand curve
Demand is $P = 20 - 2Q$. Find marginal revenue at $Q = 3$, and the quantity where MR is zero.
- $MR = 20 - 4Q$. At $Q = 3$: $MR = 20 - 12 = \$8$, while the price is $20 - 6 = \$14$.
- $MR = 0$ when $4Q = 20$, so $Q = 5$, the middle of the demand line (it reaches the quantity axis at 10).
Answer: \$8 at $Q = 3$; zero at $Q = 5$.
Common mistake
Setting marginal revenue equal to price, as for a price taker. That forgets the revenue lost on the units that could have sold at the higher price. Check: for linear demand, MR must hit the quantity axis halfway to where demand does.