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A $60 coat, half price, and then another 20% off at the till. Almost everyone expects to pay $18. You pay $24 — and the shop has not cheated anybody.
Look closely at any sale sign and you'll find it is never just a price. It's a price and something to compare it to.
"Was $80, now $50." "Half price." "30% off." "$50 — save $30!"
One of those two numbers is what you will hand over. The other one is there to tell you how to feel about the first one. And unlike the price you pay, the comparison number does not have to be a thing that ever happened to you.
Only one number on a sale sign is a price. The other is a story about a price.
Shops know something about how people judge value: we are terrible at deciding what a thing is worth on its own, and very quick at deciding whether one number is smaller than another number sitting right beside it.
So the higher number gets put right beside it. Psychologists call that first number an anchor — once you have seen it, every other number in the conversation is judged against it, whether you want it to be or not. $50 feels generous next to $80 and mean next to $35, and it is the same $50.
This has been regulated for a long time, precisely because it can be abused. In the United States the Federal Trade Commission's rules on pricing say a "was" price has to be bona fide — a real price the item was genuinely offered at, openly, for a reasonably substantial period. Inventing a high price so you can advertise a big reduction from it makes the bargain a false one under those rules.
Which means the honest question at a sale rail is never "how big is the reduction?" It is: would I pay this price, today, for this thing, if no other number were printed next to it?
A shop hangs a jacket on the rail at $200. For two weeks, nobody buys one. Then the tag changes to "$200 — now $90". What does the $200 actually tell you?
Now the arithmetic — and the mistake nearly everyone makes, including plenty of adults holding the coat.
A sign says 50% off. At the till a second sign says an extra 20% off sale items. Your brain adds them: 50 and 20 is 70, so this coat is 70% off.
It is not. It is 60% off, and it will be 60% off every single time this pair of numbers appears together, in any shop, anywhere.
The reason is the one sentence worth taking from this whole episode: a percentage is always a percentage OF something, and the two discounts are not taken from the same something.
The ticket says $60. Press through the two discounts one at a time and watch what each one is actually calculated from.
Taking 50% off and then another 20% off did not come to the same thing as taking 70% off in one go. What is the actual reason?
Same skill, different aisle.
Almost everybody believes that the bigger box is the cheaper one — buy in bulk, save money. It is often true. It is not a rule, and shops know you think it is one.
The only way to settle it is to stop comparing prices and start comparing unit prices: what the thing costs per gram, per 100 g, per litre, per sheet. A unit price ignores how big the box is, which is exactly what makes two different-sized boxes comparable at all.
Most shelf labels print one in small type near the corner. Here are three real-shaped boxes of the same cereal.
Three sizes of the same cereal. To compare them, turn each one into the cost of a single 100 g — price divided by the number of 100 g portions in the box.
The middle box is the cheapest cereal on the shelf. The giant family box costs exactly the same per 100 g as the smallest one — you are paying the same rate for the privilege of carrying more of it home. This is not a trick anyone is playing on you. It is just that box size and value are two separate things, and only one of them is printed in large friendly numbers.
The prices climb steadily left to right, which is what makes the assumption so easy to fall into. The unit prices do not.
| Box size | Cost per 100 g |
|---|---|
| 400 g box | 80 |
| 750 g box | 70 |
| 1,200 g box | 80 |
Some things printed on a shelf let you work out what you will pay. Others cannot, no matter how hard you stare at them. Sort them, and read why.
Tap an item, then tap where it belongs
A 500 g bag of rice costs $4.00. A 2 kg bag of exactly the same rice costs $15.00. Which is cheaper per 100 g?
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Former-price claims: US Federal Trade Commission, Guides Against Deceptive Pricing, 16 CFR Part 233. Section 233.1 treats a 'was' price as a legitimate basis for comparison only where it is the actual, bona fide price at which the article was openly offered to the public for a reasonably substantial period; a price inflated artificially so a large reduction can then be advertised makes the bargain a false one. Anchoring — the tendency to judge a number against the first number seen rather than on its own — is a long-established finding in the judgement-and-decision-making literature, originating with Tversky and Kahneman's 1974 work on judgement under uncertainty. Stacked-discount arithmetic, worked in full: $60 ticket, less 50% ($30) = $30; less a further 20% of $30 ($6) = $24. Total reduction $36, which is 60% of $60. Equivalently 0.50 x 0.80 = 0.40 of the original price. Unit-price example (illustrative shelf prices, arithmetic exact): 400 g at $3.20 = 80c per 100 g; 750 g at $5.25 = 70c per 100 g; 1,200 g at $9.60 = 80c per 100 g. Check-3 example: 500 g at $4.00 = 80c per 100 g; 2,000 g at $15.00 = 75c per 100 g.