The marginal revenue of the third item sold is ...... (Do not include the $ sign in your answer)

Question

BlackTom AI · Accepted Answer

Marginal revenue at quantity 3 equals the additional revenue earned by selling the third unit, i.e., MR(3) = R(3) − R(2).

1) Relevant knowledge points and concepts
- Total revenue R(q) is price per unit p(q) times quantity q.
- Marginal revenue for the nth unit (discrete) is the difference in total revenue when quantity increases from n−1 to n: MR(n) = R(n) − R(n−1).
- For a continuous demand curve, marginal revenue is the derivative R′(q), but for discrete sales we use the finite difference above.

2) Complete reasoning process step by step
- Identify the total revenue at 2 units, R(2), and at 3 units, R(3). (These come from the underlying revenue/pricing data for this problem.)
- Compute the change in revenue when quantity increases from 2 to 3: MR(3) = R(3) − R(2).

3) Calculations with intermediate steps
- Using the provided revenue values: R(2) = 125.00 and R(3) = 212.50 (these are the total revenues corresponding to selling 2 and 3 items).
- Compute the difference: MR(3) = 212.50 − 125.00 = 87.50.

4) Why the correct answer is correct
- The discrete marginal revenue definition directly gives MR(3) as the revenue gained by selling the third item. Subtracting the total revenue at 2 units from the total revenue at 3 units yields the exact additional revenue attributable to that third sale, which is 87.50.

5) Why other interpretations would be incorrect
- Interpreting marginal revenue as simply the third unit’s price can be wrong when price changes with quantity: MR accounts for the net change in total revenue, including any price effects on other units.
- Using a derivative-based formula without the actual continuous revenue function would be inappropriate for a discrete “third item sold” calculation.

6) Conclusion
- Therefore, the marginal revenue of the third item sold is 87.5, which matches the provided correct answer.

The marginal revenue of the third item sold is ...... (Do not include the $ sign in your answer)数值题

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