The steps below show why marginal revenue (MR) equals the market price p for a price-taking firm. One step is missing:
Step 1: Output rises from q1 to q2, and every unit is sold at the market price p.
Step 2: The change in total revenue is pq2 − pq1 = p(q2 − q1).
Step 3: ________
Step 4: So, MR = p.
Which of the following is the missing Step 3?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → MR = change in total revenue ÷ change in output = p(q2 − q1)/(q2 − q1).
MR is the change in total revenue divided by the change in output. Dividing p(q2 − q1) by (q2 − q1) leaves p.
Option (1) MR = total revenue ÷ output = pq2/q2, the revenue per unit sold. — Incorrect. Total revenue divided by output is average revenue, not the change in revenue from extra output.
Option (2) MR = change in total revenue ÷ change in price, with the price fixed at p. — Incorrect. MR is measured per unit change in output. The price does not change here, so dividing by a change in price makes no sense.
Option (3) MR = total revenue − total cost at q2, the gain from the last unit. — Incorrect. Total revenue minus total cost is profit.
Option (4) MR = change in total revenue ÷ change in output = p(q2 − q1)/(q2 − q1). — Correct. This follows the meaning of MR and gives p in Step 4.
NCERT (2026-27): “4.2 Revenue The marginal revenue (MR) of a firm is defined as the increase in total revenue for a unit increase in the firm’s output. … Consider the situation when the firm’s output changes from q1 to q2. Given the market price p, MR = (pq2 –pq1)/ (q2 –q1) = [p (q2 –q1)]/ (q2 –q1) = p Thus, for the perfectly competitive firm, MR=AR=p” |