AP MicroeconomicsMarket Structures
Marginal Revenue Curve Twice as Steep
For a single-price monopolist with a straight-line demand curve, the marginal revenue curve has the same intercept but twice the slope, hitting the quantity axis at half the demand's intercept.
Because a single-price seller must lower price on every unit to sell one more, marginal revenue falls faster than price. With linear demand P = a − bQ, marginal revenue is MR = a − 2bQ: same vertical intercept (a), double the slope, so it reaches the horizontal axis at half the output where demand does. This 'twice as steep, half the quantity' rule is a fast graphing shortcut for monopoly and other price-maker diagrams and explains why MR lies below demand.
Formula / Example
If P = a − bQ, then TR = aQ − bQ², MR = a − 2bQ (twice the slope; x-intercept at half of demand's).