The relationship between the marginal revenue (MR) and the average revenue(AR) of a monopolist is that the marginal revenue curve____

Analyze the question: It asks how a monopolist's MR curve relates to its AR curve.

Concept: A monopolist is the only seller, so it faces the whole market demand curve. To sell more, it must lower the price. This has two consequences:

• The AR curve (which is the same as the demand curve) slopes downward to the right.
• Lowering the price applies to all units sold, not just the extra unit. So the extra revenue from one more unit (MR) is always less than the price (AR).

Step-by-step working: Take a linear demand curve: P = a − bQ

1. AR = P = a − bQ
2. TR = P × Q = aQ − bQ²
3. MR = d(TR)/dQ = a − 2bQ

Compare the two:

• Both start at the same point on the price axis (intercept a).
• The MR curve has twice the slope of the AR curve (−2b compared with −b).
• So MR falls faster and lies below AR at every positive output.

Numerical check: Suppose P = 10 − Q.

• Q = 1: TR = 9, AR = 9
• Q = 2: TR = 16, AR = 8, MR = 16 − 9 = 7
• Q = 3: TR = 21, AR = 7, MR = 21 − 16 = 5

MR (7, 5) is less than AR (8, 7), and both fall as output rises.

Checking the options:

• A. Wrong, because MR is below AR, not above.
• B. Correct. MR slopes downward to the right and lies below the AR curve.
• C. Wrong, because the curves are identical only under perfect competition, where both are horizontal.
• D. Wrong, because MR is not vertical, and AR is not horizontal for a monopolist.

Answer: B

Exam tip: Remember "Monopoly: MR is below AR and twice as steep." In perfect competition, AR = MR = price, a horizontal line. In monopoly, MR drops faster than AR.