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

Question

BlackTom AI · Accepted Answer

A monopoly faces the market demand curve P(Q); marginal revenue (MR) is the change in total revenue from selling one more unit. For a downward-sloping demand, MR lies below the demand curve. 1) Relevant knowledge points: - Demand curve: P = f(Q), price consumers will pay for each quantity. - Total revenue (TR) = P(Q) × Q. - Marginal revenue MR = d(TR)/dQ. For a linear, negatively sloped demand, MR has the same intercept but twice the slope in magnitude, placing it below demand for any positive Q. - Intuition: to sell an extra unit a monopolist must cut price on all units, so the revenue gained on the extra unit is partly offset by lower revenue on previous units → MR < P. 2) Step-by-step reasoning and 3) calculations: - Let linear demand be P(Q) = a − bQ, with a,b > 0. - TR(Q) = P(Q) × Q = (a − bQ)Q = aQ − bQ^2. - Differentiate: MR(Q) = d(TR)/dQ = a − 2bQ. - Compare MR to price: P(Q) − MR(Q) = (a − bQ) − (a − 2bQ) = bQ > 0 for Q > 0. Thus MR(Q) < P(Q) for all Q > 0; they coincide only at Q = 0 (both equal a). 4) Why the correct answer is correct: Because MR is the derivative of TR and for a downward-sloping demand the MR curve falls faster (steeper negative slope) and lies below the demand (price) curve for positive output. This reflects the loss on existing units when lowering price to sell more. 5) Why other options are incorrect: - b (Above the demand curve): violates MR < P for downward-sloping demand; MR cannot be above price. - c (Above the average cost curve): MR and average cost are different concepts; MR need not be above AC and typically lies unrelatedly below demand—this option is irrelevant. - d (To the right of the demand curve): curves are plotted in price-quantity space; "to the right of" is meaningless here—MR is another curve in the same plane and lies below demand, not simply shifted right. 6) Conclusion: Therefore the marginal revenue curve lies below the demand curve, matching answer a.

Where does the marginal revenue curve lie on a monopoly diagram?单项选择题

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