Unit-price inversion
A Socratic walk-through of unit-price inversion — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why does the larger pack on the shelf sometimes cost more per unit than the small one?
Everyone shops by a rule they were never taught: the bigger pack is cheaper per unit. It is a good rule, and most of the time the shelf obeys it. Then you find the 750g jar at a higher price per hundred grams than the 500g jar sitting beside it, and the rule has not merely failed — it has run backwards.
The tempting reading is that someone is cheating you. Worth testing, because that reading makes a prediction: expose the arithmetic and the inversion should die. Unit prices are printed on the shelf edge by law across the EU, in Australia, and in many US states. The inversions are still there. So concealment cannot be the whole story, and we need to ask what else could put that number the wrong way round.
Reasoning it through
REASONING #Start by noticing that the rule is a claim about cost being used as a prediction about price. Cost per unit does usually fall with size — one lid, one label, one filling operation spread over more product. But price is not cost, and the gap between them is where everything interesting lives.
First, is the inversion even a policy? Often it is not. It is a snapshot. Regular prices in a category are usually ordered sensibly, and then the small size goes on promotion for a fortnight. For those two weeks the ratio flips, and the shopper who checks that day records a surcharge that will be gone by the next visit. A good share of what people photograph and post is this: a temporary deal on one size, not a decision about the other. That alone should slow us down before reaching for malice.
Second, cost is not as monotone as the rule assumes. Savings from scale run out early while new costs appear: the largest format turns over more slowly, takes more shelf per pound of sales, and on anything perishable risks being marked down or binned. Stock that sells slowly needs a wider margin to earn the same return on its space. So a genuine cost-driven surcharge is possible with nobody intending a trick.
Third — and this is the mechanism the cheating story misses — price sensitivity does not track size. It tracks knowledge. Shoppers carry a rough memory of the price of the size they buy every week, and almost none for sizes they never buy. That is why retailers price the familiar formats thin and take margin on the unusual ones. Notice what this predicts: the surcharge should attach to whichever size is rare in that category, not always to the large one. And it does. In categories where the huge pack is the ordinary weekly purchase — pet food, nappies, laundry powder — the bulk discount is usually intact, and it is the little emergency-sized box that is dear. The inversion appears where the big pack is the occasional buy.
Fourth, the rule itself is a target. A shopper who knows bigger is cheaper stops computing. That splits the shelf's audience into people who check and people who infer, and a retailer facing both can hold a competitive price on the size the checkers watch while resting a little extra on the size the inferrers assume is safe. This is price discrimination sorted by attention rather than by quantity — which is exactly why printing the unit price helps without fixing it. The number on the label removes the excuse, not the habit.
The analogy
THE ANALOGY #Think of the two currency-exchange windows a traveller meets: the one in the airport terminal and the one on the high street. The airport rate is worse, and not because euros cost more inside the terminal. It is worse because the person standing there has already sorted themselves into the group that is not going to compare. The window is not selling currency so much as selling to whoever walked up to it — and the pack size on a shelf works the same way, sorting shoppers by how much checking they were ever going to do.
the traveller can always walk to the other window and get an identical product, whereas pack sizes are not freely substitutable — storage, household size and how fast the thing spoils genuinely constrain which one you can use, so the cheaper unit price is sometimes not a real option at all.
Clarifying the model
THE MODEL #Two refinements hold the pieces together.
The first is that intent is largely unnecessary here, and probably unknowable from outside. Whether a given surcharge was designed or fell out of promotion calendars, category-management software and slow stock turn is genuinely argued in the retailing literature, and a shopper cannot tell them apart from the shelf. The incentive is not in doubt: nothing punishes the surcharge as long as it lands on the people not looking.
The second is that unit price is a better rule than pack size, but it is not the rule. The lowest price per gram is only cheapest if you use all the grams. A large pack that goes stale, ties up cash, or simply gets eaten faster because it is there can be dearer in practice than the number implies. And treat any single figure for how common surcharges are with suspicion: studies report wildly different rates depending on whether promotions, flavour variants and multipacks count as comparable. The mechanism is far better established than its frequency.
A picture of it
THE PICTURE #How to readStart at the rounded terminal at the top — the thing you actually observed — and work down through the three diamonds, which are the questions that tell the causes apart. The first branch leads to a dated artefact rather than a policy, and its back-edge through the promotion store shows why the same shelf looks different next week. The two lower branches separate a surcharge you are paying for real handling costs from one you are paying for not checking. All three paths converge on the same subroutine, because the reader's move is identical whichever cause applies.
What became clearer
WHAT CLEARED #The bulk discount is a regularity, not a law, and the exceptions are not one thing. Some inversions are a promotion caught mid-cycle; some are the genuine cost of carrying a format that sells slowly and spoils; and some are a quiet charge levied precisely on the shoppers who trust the regularity enough to stop looking. That last one explains why mandatory unit-price labelling helped and did not cure: the surcharge was never hidden in the arithmetic, it was resting on the fact that most people were not going to do the arithmetic at all.
Where to go next
ONWARD #- Why supermarkets keep so many sizes of the same product when a few would do.
- How "known-value items" get chosen, and what happens to the price of everything else once they are.
Key terms
TERMS #| Term | What it means |
|---|---|
| Unit price | price expressed per standard quantity, such as per 100g or per litre, so packs of different sizes can be compared. |
| Quantity surcharge | the case where a larger pack carries a higher unit price than a smaller one of the same product. |
| Known-value item | a product whose price a large share of shoppers can recall, and which retailers therefore price competitively as a signal. |
| Second-degree price discrimination | charging different amounts by letting buyers sort themselves between versions, rather than by identifying them directly. |
Every term the collection defines is gathered in the glossary.