Lesson 1.2 · Unit 1 · CA HSS 12.1.2
Opportunity cost, marginal benefit and marginal cost
If every choice forgoes an alternative, the real cost of anything is the alternative given up. That idea, combined with the habit of evaluating one additional unit at a time, is most of what economic reasoning consists of.
- Opportunity cost is the value of the next best alternative forgone when a choice is made.
- It is the next best alternative, not all of them, since you could only have done one other thing with the resource.
- Opportunity cost includes what is not paid out, such as the wages a full-time student gives up, which is why the cost of a year of study exceeds the tuition.
- Marginal means one more unit, so marginal cost is the cost of producing one more and marginal benefit is the value of consuming one more.
- The decision rule is to do it while marginal benefit exceeds marginal cost, and to stop when marginal cost overtakes marginal benefit.
- Marginal benefit usually falls as quantity rises, because the first unit satisfies the most urgent want and later units satisfy less urgent ones.
- Sunk costs are already spent and cannot be recovered, so they belong in no decision about what to do next.
- The production possibilities frontier shows the maximum combinations of two goods obtainable from fixed resources, and its slope at any point is the opportunity cost of one good in terms of the other.
Where students lose marks: including sunk costs in a marginal decision. Money already spent is gone under every option, so it cannot distinguish between them.
Constructed data. An invented bakery deciding how many cakes to bake. Work the margin, then test the sunk cost trap.
| Cake | Marginal cost | Marginal benefit (price received) |
|---|---|---|
| 1st | 9 | 25 |
| 2nd | 10 | 25 |
| 3rd | 12 | 25 |
| 4th | 16 | 25 |
| 5th | 23 | 25 |
| 6th | 34 | 25 |
| 7th | 50 | 25 |
Step one: apply the rule cake by cake. Cake one earns 25 and costs 9, a gain of 16. Cake two gains 15, cake three gains 13, cake four gains 9, cake five gains 2. Cake six loses 9 and cake seven loses 25.
Step two: state the answer. Bake five. The fifth cake is still worth baking because it adds 2, and the sixth is not because it subtracts 9. The rule is to continue while marginal benefit exceeds marginal cost, not to bake as many as possible.
Step three: total the result. Gains of 16, 15, 13, 9 and 2 add to 55. Baking six would give 46 and baking seven would give 21, so the rule genuinely maximizes. The arithmetic confirms the rule rather than merely restating it.
Step four: explain why marginal cost rises. The baker uses the most convenient oven space first, then less convenient space, then pays overtime, then buys ingredients at short notice at higher prices. Each additional unit draws on progressively worse alternatives, which is the general reason marginal cost rises.
Step five: introduce the sunk cost. Suppose the baker already paid 400 for a new mixer that cannot be returned. Does that change the answer?
Step six: work it out. The 400 is spent under every option: baking zero, five or seven cakes leaves it equally gone. Since it is identical across all the alternatives, it cannot make any of them better than another. The answer is still five, and the baker's total is 55 minus 400, which is a loss of 345 for the day.
Step seven: state the uncomfortable implication. Baking more cakes to justify the mixer makes the loss larger, not smaller. Baking seven gives 21 minus 400, a loss of 379. The instinct to recoup a sunk cost by doing more is exactly the error the concept warns against.
Step eight: connect to opportunity cost. Suppose the baker could instead spend the day teaching a class for 40. That 40 is the opportunity cost of baking, so the relevant comparison is 55 against 40, and baking wins by 15. The 400 mixer never enters either side of the comparison.
Questions 1 to 5 are recall. Questions 6 to 10 ask for reasoning.
- Define opportunity cost.
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The value of the next best alternative forgone when a choice is made
- Define marginal cost and marginal benefit.
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The cost of producing one more unit and the value of consuming one more unit
- State the marginal decision rule.
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Continue while marginal benefit exceeds marginal cost; stop when marginal cost overtakes it
- Define a sunk cost.
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A cost already spent that cannot be recovered
- What does the slope of a production possibilities frontier represent?
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The opportunity cost of one good in terms of the other
- Work through the bakery decision and justify the stopping point.
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Cake one gains 25 minus 9, which is 16; cake two gains 15; cake three 13; cake four 9; cake five 2. Cake six costs 34 against a benefit of 25, losing 9. So the baker stops at five. Total gain is 16 plus 15 plus 13 plus 9 plus 2, which is 55, against 46 for six cakes and 21 for seven. The rule maximizes, and the arithmetic confirms it. Five cakes, giving 55 against 46 for six and 21 for seven
- Why does marginal cost rise with each additional unit?
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Because a producer uses the best available resources first and progressively worse ones afterward. The baker fills the most convenient oven space before the awkward space, works normal hours before paying overtime, and buys ingredients on the regular schedule before paying short-notice prices. Each extra unit therefore draws on a less favorable alternative than the one before, so the cost of producing it is higher. Best resources are used first, so later units draw on worse alternatives
- Explain why the 400 mixer does not change the answer.
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Because it is spent identically under every option. Baking zero cakes, five cakes or seven cakes all leave the 400 equally gone and unrecoverable, so it cannot make any option better or worse than another. A figure that appears the same on both sides of a comparison cancels out of it. The best decision remains five cakes, and the day's result is 55 minus 400, a loss of 345. It is identical under every option, so it cannot distinguish between them
- Why does baking more to justify the mixer make things worse?
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Because the sixth and seventh cakes lose money on their own terms, costing 34 and 50 against a benefit of 25 each. Baking seven yields 21 rather than 55, so the day's loss deepens from 345 to 379. The mixer is not recovered by any of this, since it was never recoverable. Trying to justify a past expenditure by adding further loss-making activity is the classic sunk cost error. The extra cakes lose money, deepening the loss from 345 to 379
- Set the decision up as an opportunity cost comparison.
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If the baker's next best use of the day is teaching a class for 40, then 40 is the opportunity cost of baking. The comparison is the 55 that optimal baking yields against the 40 from teaching, so baking is better by 15. Notice that the 400 mixer appears on neither side, since it is gone whichever the baker does, and that the relevant alternative is the single next best one rather than every option that existed. 55 from baking against 40 from teaching, with the mixer on neither side