Thirty Notebooks, Twenty Bookmarks
Two seventh-grade classes run a market simulation during one 50-minute period. Class A can produce either 40 notebooks or 20 bookmarks. Class B can produce either 15 notebooks or 15 bookmarks, because B's equipment is slower for notebooks. Materials are limited to 60 sheets of card stock and one shared set of cutting tools.
Right now each class splits its time evenly: A makes 20 notebooks and 10 bookmarks; B makes 7 notebooks and 8 bookmarks. That is 27 notebooks and 18 bookmarks in total. The school fair needs 30 notebooks and 20 bookmarks.
One student proposes that everyone simply work faster. Another proposes that the classes specialize and trade. The teacher adds a rule: any student who produces more than the class quota earns 5 extra-credit points, but all items go to the fair.
1. Use opportunity cost to show which class should specialize in which good, then give a production plan that meets the fair's needs exactly.
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For Class A: 40 notebooks cost 20 bookmarks, so 1 notebook costs 0.5 bookmark, and 1 bookmark costs 2 notebooks. For Class B: 15 notebooks cost 15 bookmarks, so 1 notebook costs 1 bookmark and 1 bookmark costs 1 notebook.
A gives up less to make a notebook (0.5 bookmark versus B's 1), so A has the comparative advantage in notebooks. B gives up less to make a bookmark (1 notebook versus A's 2), so B has the comparative advantage in bookmarks even though A is faster at both.
Plan: B spends the whole period on bookmarks, producing 15. A spends three-quarters of the period on notebooks (30) and one quarter on bookmarks (5). Total: 30 notebooks and 20 bookmarks, exactly the target, with nobody working faster and no extra materials.
Check the reverse: if A made only bookmarks and B only notebooks, the classes would get 20 bookmarks and 15 notebooks - short by 15 notebooks.
2. Why does working faster fail to solve the problem, and what does the successful plan show about scarcity and trade?
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Working faster helps only if it genuinely raises output per minute, and the plan meets the target without any productivity change, so effort is not the binding limit. The binding limits are the 50-minute period, the shared cutting tools, and the 60 sheets of card stock. Speed also has a cost: rushed cutting produces errors and waste, and with one shared tool set, faster work by one class can slow the other.
Scarcity means the classes cannot have every combination they might want; their possibilities lie on the line between the two endpoints for each class. Choosing more notebooks means giving up bookmarks unless trade occurs.
Trade relaxes each class's own limit, because each can consume beyond its own production line. Under the even split the classes were short 3 notebooks and 2 bookmarks. Under specialization with trade, both shortfalls disappear - and that gain comes from reallocating time by comparative advantage, not from effort.
3. The extra-credit rule awards 5 points per item produced above quota, but all items go to the fair. Predict one unintended consequence and design a better rule.
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The reward is per item, but the fair's need is a specific mix. Students facing this rule will overproduce the easy good - bookmarks - because each one earns the same 5 points, so the class can pile up points while the fair still lacks notebooks. A second consequence: with only 60 sheets and one tool set, students have an incentive to hoard materials to protect their own point totals, which lowers total output. A third: speed replaces quality, so more items are cut badly.
Better designs: pay a group bonus when the 30/20 target is met, so points track the actual goal; or award points for the surplus that the two classes agree to trade, which rewards the coordination the lesson is about; or announce quotas by good in advance so the incentive matches the need.
The general principle: incentives shift behaviour, and a reward that does not match the goal produces effort in the wrong direction. The original rule is not cruel, just badly aligned.