Relationship Between AR and MR

The AR–MR relationship looks quite different once the firm is no longer a pure price taker.

Under perfect competition, as shown in the previous section, the firm faces a perfectly horizontal (infinitely elastic) demand curve at the ruling market price. AR and MR coincide and are both equal to that constant price — a single horizontal straight line.

Under imperfect competition (monopoly, monopolistic competition, oligopoly), the firm faces a downward-sloping demand curve — to sell more, it must lower the price on all units sold, not just the extra one. Because the price cut applies to every unit, not only the marginal one, MR falls faster than AR (= price) as output rises, and the MR curve lies below the AR curve at every output level beyond the very first unit. A useful graphical rule: whenever the AR curve is a straight line, the MR curve bisects the horizontal distance between the price axis (Y-axis) and the AR curve at every output — MR's slope is twice as steep as AR's.

Consider a firm facing the demand relation $P = 30 − 2Q$:

Notice that at the very first unit, MR equals AR (both ₹28) — this always happens for the first unit, since the whole of TR at Q = 1 is itself the 'addition' to a starting TR of zero. From the second unit onward, MR is consistently below AR (24 < 26, 20 < 24, 16 < 22, 12 < 20, 8 < 18) and falls faster, exactly as the rule predicts. …