Price Discrimination: Charging Different Buyers Differently

Price discrimination is charging different buyers different amounts for substantially the same thing. Arthur Cecil Pigou set out its three degrees in The Economics of Welfare, 1920. Most readers assume it means charging more. Charging differently need not mean charging more: a flat charge and a tiered one can collect the identical total. Two tiers change which buyers carry the charge, and whether the arrangement earns anything depends on what a single rate would have collected.

Two things sit underneath that. The first is arithmetic already established: a charge is a rate applied to an amount, and the money that arrives is the two multiplied. The second is the part readers skip. A rate does not have to be one number. The moment a seller applies one rate to part of what passes through and a different rate to the rest, the total stops being a single multiplication. Who pays separates cleanly from how much arrives. The two are different questions with different answers, and they are routinely confused for one another.

What is price discrimination, and who set out its three degrees?

Price discrimination is charging different buyers different amounts for substantially the same thing. Hold on to the word substantially. Not a different thing, not a different quantity of attention, not next week instead of today: the same thing, at the same time, at two prices, to two buyers. A vegetable seller who quotes one number to a customer she has known for ten years and a higher number to a stranger who has clearly just moved into the locality is doing it, in the plainest possible form, without a rate card and without a name for it.

Arthur Cecil Pigou set out the first, second and third degrees of price discrimination in The Economics of Welfare, published in 1920, and the three degrees are his. The three degrees have been taught for a century as though they were a natural feature of the landscape, and they are not. The degrees are one man's classification, and naming him costs a sentence and tells a reader exactly which book to open.

Pigou's first degree is charging every buyer their own amount, the most that particular buyer would part with. Reading each buyer individually is hard, so the first degree is the pure case and the rare one. The second degree is charging by the quantity or the version taken, with the buyer choosing which one to take: a slab rate on bulk orders, a larger pack at a lower rate per unit, a cheaper edition with something left out. The third degree is charging by an observable group the seller can identify from the outside: a morning show at a cinema, a rate for students, a different rate in a different town.

The clean way to hold the three apart is to ask who does the sorting. In the first degree the seller reads each buyer and sets a number for that buyer. In the second degree the buyer sorts itself by choosing between the versions on offer. In the third degree the seller sorts buyers by a label it can see without asking. The sorting question separates all three, and it beats memorising the ordinals. In a real business the analyst is handed a rate card and asked which of the three is going on.

What has to be true for it to work at all?

Three conditions, and a seller needs all three at once. Take any one of them away and the arrangement either collapses or was never available in the first place.

The first condition is that buyers must actually differ in what they will pay. If every buyer would pay the same, two rates are two ways of writing one rate, and one of them is simply money left on the counter or money never collected. The second condition is that the seller must be able to tell the two groups apart, or else get them to sort themselves. A rate for a segmentA group of buyers a business chooses to treat as one, because they behave similarly enough that one description covers them. How segments are chosen and described is covered under Customers and Brands. the seller cannot identify is a rate nobody can be charged.

The third condition is that resale between the two groups must be hard, and it is the one readers forget. Think about what happens if it is easy. A rice wholesaler quotes a lower rate on fifty bag lots and a higher rate on single bags. Two small shopkeepers who each want ten bags discover they can club together, buy fifty through one of them, and split the load in the lane behind the godown. The cheap tier has begun selling to the dear tier. Every buyer drifts to the low rate, the high rate applies to nobody, and the seller is left with one rate it did not choose. The drift has a name of its own: it is arbitrageBuying something where it is cheap and selling it where it is dear, so the two prices are pulled together. The word is used across markets and is covered under trading and markets., and it is the thing the third condition exists to prevent.

The resale condition explains why the practice shows up where it does. A service is hard to resell: a haircut, a night in a room, a seat in a coaching class, a payment processed through a marketplace. A physical good in a sack is easy to resell. Any business charging two rates usually has something structural stopping the cheap side from selling on: a seat tied to a name, a licence tied to an account, a rate tied to a volume that the buyer cannot fake, or simply the fact that the thing being sold disappears the moment it is used.

Does charging differently mean charging more?

Most readers go wrong at this point, so it is worth working slowly on real figures. Setu Bazaar, an invented marketplace, has Rs 500 crore of flow passing through it in the year and charges a flat 4.00 per cent on that flow. Four per cent of Rs 500 crore is Rs 20 crore, and that is the whole of its charge for the year. The flat 4.00 per cent is its take rateThe slice a marketplace retains for itself out of everything transacted across it. The take rate is covered under Business Fundamentals and Models., and it applies to every rupee of flow regardless of which merchant produced it.

Now split the merchants into two groups of equal size by flow: Rs 250 crore of flow from the smaller merchants and Rs 250 crore from the larger ones. Charge the smaller merchants 5.00 per cent and the larger merchants 3.00 per cent. Five per cent of Rs 250 crore is Rs 12.5 crore. Three per cent of Rs 250 crore is Rs 7.5 crore. Add them and the charge for the year is Rs 20 crore.

The two arrangements collect exactly the same amount. Discrimination changed who pays and left what was collected alone. One group is now paying a full percentage point more than it did and the other a full percentage point less, and the money arriving at Setu Bazaar has not moved by a single rupee.

Before that is filed away as a surprising result, it is worth looking at how it was built, because it is not a discovery. The charge under two tiers is the flow multiplied by the flow-weighted average of the two rates. On halves of equal size that weighted average is the ordinary average of 5.00 and 3.00, or 4.00. So the two-tier total had to equal the flat total the moment those particular rates were placed on those particular halves. The agreement between the two totals is an identity that follows from the construction, not a coincidence anybody discovered, and it holds only because the two rates average to the flat rate on equal halves. An account that presents it as a surprise deserves suspicion.

Why does the agreement break the moment the split is uneven?

Move the split and watch the identity go. Suppose 60 per cent of the flow sits with the smaller merchants, so Rs 300 crore is charged at 5.00 per cent and Rs 200 crore at 3.00 per cent. The two tiers bring Rs 15 crore and Rs 6 crore, or Rs 21 crore in total. The flat rate collects Rs 1 crore less. Push it the other way, with Rs 200 crore at 5.00 per cent and Rs 300 crore at 3.00 per cent, and the total is Rs 10 crore plus Rs 9 crore, or Rs 19 crore. The flat rate now collects Rs 1 crore more.

The two arrangements agree at exactly one split and disagree everywhere else. The equality is therefore a property of the numbers chosen rather than a property of tiering. The flow-weighted average rate is doing all the work: at the even split it is 4.00 per cent, at the sixty forty split it is 4.20 per cent, and at the forty sixty split it is 3.80 per cent. Multiplying any of those by Rs 500 crore gives the answer without touching the tiers at all.

When does a discounted tier bring in money a single rate could not?

Everything so far has assumed that every merchant transacts whatever the rate. Drop that and the arrangement starts to do real work. Suppose that at a flat 4.00 per cent the arrangement is not worth the while of Setu Bazaar's larger merchants, so they take their volume elsewhere and do not transact at all. Under a single flat rate, then, Setu Bazaar is not charging 4.00 per cent on Rs 500 crore. The marketplace is charging 4.00 per cent on the Rs 250 crore the smaller merchants bring, and it collects Rs 10 crore.

Under the two tiers, 3.00 per cent is a rate the larger merchants will transact at, so they stay and bring Rs 7.5 crore. The smaller merchants pay 5.00 per cent and bring Rs 12.5 crore. Setu Bazaar collects Rs 20 crore instead of Rs 10 crore, and the Rs 7.5 crore that the discounted tier produced was never available under one rate at any level.

A discounted tier is not revenue given away if the alternative was no transaction at all. The whole case for a lower tier sits in that one sentence, and the reverse is worth saying too: a discount only costs a seller something when the buyer taking it would have transacted anyway. The same sentence covers a coaching class that keeps one concession seat for a student who could not otherwise attend. The class collects less from that seat than from the others and more than it would collect from an empty chair, and both halves of that are true at once.

Now the part that has to be said as loudly as the finding. Whether the larger merchants would really have walked away at 4.00 per cent was written into this illustration as an assumption, and it is not a finding of any kind. Nobody observed it. The assumption was written into the example so the mechanism would be visible. The counterfactualWhat would have happened under the other arrangement, which nobody gets to observe because only one arrangement actually ran. A counterfactual is reasoned about and never measured. is unobservable by construction: only one arrangement runs, so the other one leaves no trace to check. Every claim that a tier earned its keep rests on a story about what would otherwise have happened, and that story is the part to interrogate.

How does a seller sort buyers it cannot read?

The second condition asked whether the seller can tell the two groups apart. Very often it cannot. A marketplace does not know which merchant would have walked away at 4.00 per cent, a publisher does not know which reader would have paid double, and a coaching class cannot see a household's budget. A buyer facing two rates has every reason to claim the cheaper one, so asking is useless.

So the seller stops trying to observe and starts trying to make the buyer reveal itself. The seller offers versions that differ in something the two groups value differently, and then lets each buyer choose. A slab rate that only rewards volume nobody small can produce. A couponA voucher giving a stated reduction to whoever presents it. The word survives from paper vouchers and now usually means a code entered at checkout. that a buyer has to hunt for and enter, at the cost of a minute of effort that a hurried buyer will not spend. A cheaper package with a feature removed. BundlingSelling several things together for one amount rather than separately. How a bundle is assembled, and what it does to a rate card, sits with Operating Model and Supply Chain. several items so that only a buyer wanting all of them takes the deal.

The versions exist to sort the buyers and not to serve them. A reduced version is therefore a common and entirely rational design rather than a lapse. The reduced version's job is to be unattractive to the group that would have paid the higher amount. If the cheaper version were nearly as good, the expensive one would empty out, and the seller would be back to one rate. Once that is seen, a great many otherwise puzzling product decisions stop being puzzling.

What does a practitioner actually ask when a rate card has two rows?

An analyst reading a marketplace, or a lender sizing how durable a charge is, does not start with whether two rates are reasonable. There is one question that finds everything, and it is this: what would this buyer have done under a single rate? Every claim a tier makes for itself rests on that answer and on nothing else, so it is the answer to hunt for and it is almost never in the document itself.

Work outwards from there. If the discounted group would have transacted anyway, the concessionA reduction from the ordinary amount granted to a named group or in a named situation. The word is used the same way for fares, fees and rates. is money the seller chose not to collect and the total falls. If the discounted group would have gone elsewhere, the concession is the only reason any of that money arrived. The two situations produce the identical rate card and completely opposite conclusions, and a rate card cannot tell them apart. Neither can a revenue line: Anjani Stationers Private Limited reported revenue of Rs 2,70,00,000/- and earnings before interest and tax of Rs 41,50,000/- for the year, and neither figure reveals whether it ran one counter rate or a counter rate and a school slab. A reported total is silent on the rate structure that produced it, so the structure has to be established separately or not claimed at all.

A seller can announce a two rate arrangement it cannot hold, so check the third condition against the business as it actually operates. Ask what physically prevents the cheap side from selling on. If the answer is a rule in a contract nobody polices, the list rateThe published, ordinary amount before any reduction. Also called the rack rate or the counter rate depending on the trade. will decay towards the discounted one over time, and the arrangement described in the rate card will stop being the arrangement in the accounts.

What does the practice not establish?

Three things, and every one of them is claimed for it somewhere. The practice does not establish that the seller earns more. The Rs 20 crore against Rs 20 crore has already settled that one. The practice does not establish that the seller can sustain the arrangement either. Sustaining it turns on the third condition holding year after year against buyers who have every reason to work around it. And whether a business is in a position to charge differently at all is a separate question about competitive position, taken up in Competitive Advantage and Moats.

Describing a charging arrangement is not endorsing it. The definition, the conditions and the arithmetic are one subject. Whether any particular arrangement is fair, or whether any law permits it, is a separate question. A conclusion that an arrangement is acceptable or unacceptable never comes from the arithmetic, and it is worth establishing what it did come from.

Setu Bazaar and Anjani Stationers Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.