Where does the marginal revenue curve lie on a monopoly diagram?

Question

BlackTom AI · Accepted Answer

Marginal revenue lies below the demand curve because a monopolist must lower price on all units to sell an extra unit, making MR less than price for any positive quantity.

1) Relevant concepts
- Demand curve (average revenue for the firm): P(Q) shows price consumers will pay at each quantity; for a monopolist average revenue = price.
- Total revenue TR(Q) = P(Q)·Q. Marginal revenue MR = dTR/dQ is the additional revenue from selling one more unit.
- For a downward‑sloping demand, MR falls faster than price and is therefore below the demand curve for Q > 0.

2) Step‑by‑step reasoning (algebraic demonstration)
- Start with a linear demand: P(Q) = a − bQ, where a, b > 0.
- Total revenue: TR(Q) = P·Q = (a − bQ)Q = aQ − bQ^2.
- Differentiate to get marginal revenue: MR(Q) = dTR/dQ = a − 2bQ.
- Compare MR to price: P(Q) = a − bQ. Subtract: P(Q) − MR(Q) = (a − bQ) − (a − 2bQ) = bQ.
- For any positive quantity Q > 0, bQ > 0, so MR(Q) = P(Q) − bQ < P(Q). At Q = 0, MR = P = a (they meet at the intercept).

3) Intermediate steps shown above (TR → differentiate → compare MR vs P).

4) Why the correct answer is correct
Because MR = P − bQ for the linear demand example, MR lies below the demand (price) curve for all positive quantities. Intuitively, selling an extra unit forces the monopolist to reduce the price on all units sold, so the incremental revenue gained is smaller than the price of that extra unit.

5) Why other options are incorrect
- a (Above the average cost curve): MR refers to revenue, not cost; it may be above or below AC depending on scale, so this is irrelevant/wrong.
- b (To the right of the demand curve): “To the right” is a spatial/horizontal statement that doesn’t describe MR’s position relative to demand; MR is a curve in the same price–quantity space.
- d (Above the demand curve): This contradicts the algebra and intuition—MR is lower than price for Q>0, not higher.

6) Conclusion
Therefore the marginal revenue curve lies below the demand curve. This matches the provided correct answer: c. Below the demand curve.

Where does the marginal revenue curve lie on a monopoly diagram?Single choice

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