Darren’s marginal benefits from a can of soda are: 1st can = $9, 2nd = $8, 3rd = $7, 4th = $6.50. At a price of $7 per can, how many cans should he buy?

Question

BlackTom AI · Accepted Answer

A rational consumer purchases additional units while the marginal benefit (MB) of the next unit is at least as large as the price. This is the key decision rule for discrete purchases.

1. Relevant knowledge points and concepts
- Marginal benefit (MB): the additional value a consumer gets from one more unit.
- Decision rule: buy another unit if MB ≥ price (since net gain MB − price ≥ 0).
- Diminishing marginal benefit: MB typically falls with each additional unit.

2. Step-by-step reasoning
Evaluate each can in order, comparing its MB to the price ($7). If MB − price ≥ 0, buying yields nonnegative net benefit; continue. Stop when MB − price < 0.

3. Calculations (all intermediate steps)
- 1st can: MB1 = $9. Compare to price $7: 9 ≥ 7. Net benefit = 9 − 7 = +$2 → buy.
- 2nd can: MB2 = $8. Compare: 8 ≥ 7. Net benefit = 8 − 7 = +$1 → buy.
- 3rd can: MB3 = $7. Compare: 7 ≥ 7. Net benefit = 7 − 7 = $0 → indifferent but acceptable to buy (MB ≥ price).
- 4th can: MB4 = $6.50. Compare: 6.50 < 7. Net benefit = 6.50 − 7 = −$0.50 → do not buy.

4. Why the correct answer is correct
The rule MB ≥ price dictates purchases. The first three cans meet this rule (MBs 9, 8, and 7 are ≥ 7). The fourth does not (6.50 < 7), so buying it would reduce total net benefit. Thus the optimal quantity is three cans.

5. Why other multiple-choice options are incorrect
- Option A (1): ignores positive net benefit from the 2nd and 3rd cans (they add +$1 and $0 respectively).
- Option C (4): includes the 4th can even though its MB < price, which would lower net benefit.
- Option D (0): implies buying none, but the first can yields +$2 net benefit, so that is suboptimal.

6. Conclusion
Following MB ≥ price yields purchasing 3 cans. This matches the provided correct answer: B. 3.

Darren’s marginal benefits from a can of soda are: 1st can = $9, 2nd = $8, 3rd = $7, 4th = $6.50. At a price of $7 per can, how many cans should he buy?单项选择题

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