Lesson preview · Thinking at the margin
Decisions at the margin
~7 min · Free to read
It’s the night before a science test, and Amara hasn’t started revising (going over her notes). Every hour she revises is an hour less sleep. How many hours should she do?
Asking “Is revision good?” won’t help her. Of course it is. A better question is smaller: is the next hour worth it?
Key Term
Marginal benefit and marginal cost
Marginal means “one more”. It’s about the next step, not everything so far. A step can be one hour, one slice or one shift.
- Marginal benefit (MB): what one more step adds. For Amara, it’s the extra test points from one more hour of revision.
- Marginal cost (MC): what one more step costs you, including what you give up. For Amara, it’s the hour of sleep she gives up. She’ll be more tired in the test, so that lost hour costs her points.
If the next step adds more than it costs (MB is bigger than MC), take it. Then ask the same question about the step after. Once a step costs more than it adds, stop.
Marginal benefit usually shrinks as you do more. In her first hour, Amara works on the topics she knows least, so she learns a lot. By her third hour she’s going over things she mostly knows, so she learns less.
Her marginal cost moves the other way: it grows. The first hour of sleep she gives up costs her a little. Give up four and she’d be worn out in the test.
So Amara should stop after three hours. Her third hour still added more than it cost (6 points against 4), but a fourth would add 4 and cost 5. Revision didn’t become useless at hour 4. It just stopped being worth what it cost.
Amara didn’t look at her total or her average. After three hours she’s 15 points better off in total, an average of 5 points an hour. Both look healthy, but neither says anything about hour 4. Totals and averages describe the hours she’s already done. When you’re deciding whether to do one more, judge that next step on its own.
Check yourself · no marks
Sam has revised for three hours and gained 6 points an hour on average. Sam says: “Revision is averaging 6 points an hour, so a fourth hour must be worth it.” What’s wrong with this?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Trap · Common Misconception
Smaller isn't the same as not worth it
Some students think you should stop as soon as the extra benefit starts to fall. Amara’s second hour added less than her first (8 points against 10), but it was still worth doing, because it cost only 3. Stop when the next step costs more than it adds, not when it adds less than the last one.
Trap · Warning
Trap: costs you can't get back
Jo pays 15 dollars for a day pass at the swimming pool, and she can’t get a refund. After an hour she’s cold and bored, and a friend invites her over. “But I paid 15 dollars!” she thinks.
That money is gone whether she stays or leaves, and so is the hour she’s already spent there. Money or time you’ve already spent and can’t get back is a sunk cost, and it shouldn’t change your decision. The only question is whether her next hour at the pool beats the next hour at her friend’s.
Practice · 1 / 6
Dev has practised the guitar for two hours today. What is the marginal benefit of a third hour of practice?
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