Two seats on the same flight, same row, same plane. One passenger paid $89 and the other $540. Neither is being cheated, and the airline has not made a mistake: the plane was priced by a computer that knows, minute by minute, how many people are still likely to book and how much each kind of traveller will bear. Walk through a supermarket and the same mind is at work in smaller ways: $2.99 instead of $3, a "premium" size next to the ordinary one, a coupon that only some people clip.
A price looks like a fact about a product. It is really a decision about who will buy it, how many, and how much of their own happiness you are going to collect. The marketing and economics behind that decision are the subject here, and it is one of the few areas where a little theory is worth money the same afternoon.
Every customer carries a private number: the most they would pay for your product. It is their willingness to pay. Line customers up from the highest number to the lowest and you have drawn the demand curve: at any price, everyone whose number is at least that price buys. Raise the price and you lose the customers at the bottom of the line; lower it and you win more, but each one pays less. The seller's problem is to pick the point on that line where the money collected is largest.
The gap between what a customer would have paid and what they did pay is their consumer surplus. Pricing is partly a negotiation over who keeps it. In the model below, 200 invented customers have willingness to pay that spreads out in the way many real markets do: a few who would pay a lot, a crowd who would pay a little. Move the price and watch revenue, profit and surplus pull against each other.
Willingness to pay of customer i out of 200 is −mean × ln((i + 0.5) ÷ 200): an exponential spread, illustrative. A customer buys if willingness to pay ≥ price.
At the defaults, a cost-plus price (cost of $20 plus half again, $30) sells to 110 people and earns $1,100 profit. The profit-maximising price is $74: it loses more than half of those customers, and earns $2,484 from the 46 who remain, in this made-up market. Now slide "how much customers value it" up to $100 and press cost-plus again. The cost-plus price is still $30 and earns $1,480; the best price has jumped to $121 and earns $6,060. That is the whole critique of cost-based pricing in one gesture.
Businesses reach for three anchors. Cost-plus adds a margin to what it cost to make; it is simple, and it ignores the customer completely, so it leaves money on the table when the product is worth more and sells nothing when it is not. Competitive pricing follows rivals; it is natural when products are alike (petrol, flights on one route) and weakest when yours is different. Value-based pricing starts from what the product is worth to the buyer, the savings or enjoyment it delivers, and charges a share of it.
| Method | Starts from | Works when | Fails when |
|---|---|---|---|
| Cost-plus | your cost | costs are high and shared by all rivals; a quote must be fast | customers would pay far more, or far less, than cost implies |
| Competitive | rivals' prices | products are near-identical | you are cheaper to make, or better, and still match them |
| Value-based | customer's gain | the benefit can be put in money (hours saved, losses avoided) | the benefit is vague or can't be shown to the buyer |
A worked number. A scheduling tool saves a clinic 10 hours a month; at $25 an hour that is $250 of staff time. A value-based price might be $60 a month: the clinic keeps most of the gain and says yes quickly. Cost-plus on a tool that costs $4 per customer a month to run would say $6. The software firm that prices at $6 has made the buyer happy and itself poor. Notice also that cost still matters, as a floor: below it, each extra sale loses money.
Raise the price and sales fall, but by how much? The answer is price elasticity of demand: the percentage change in quantity for a one-percent change in price. If it is more negative than −1, demand is elastic: a price rise loses more in volume than it gains per unit, so revenue falls. If it is between 0 and −1, demand is inelastic: customers shrug, and a rise brings in more money. Petrol and insulin for a diabetic are inelastic in the short run. A particular brand of cereal, with ten near-identical substitutes on the shelf, is elastic.
The second rule is the one practitioners use: the more elastic the demand, the thinner the margin. Supermarkets sell milk at slim margins (shoppers notice and compare) and gift cards at fat ones. The calculator uses a simple straight-line demand: 1,000 units at a price of zero, falling by 10 for every dollar.
Demand: Q = 1,000 − 10 × P. Elasticity at a point = −10 × P ÷ Q. Revenue peaks at P = $50; profit peaks at (100 + cost) ÷ 2. Illustrative.
Set the cost to $20. At $30 you sell 700 units for $21,000 of revenue and $7,000 of profit; ε is about −0.43, so demand is inelastic and a rise helps. At $50 revenue peaks at $25,000 (ε = −1) but profit is $15,000. At $60 revenue slips to $24,000 while profit rises to $16,000 (ε = −1.5), the best. Profit-maximising prices sit above the revenue-maximising one whenever costs are positive, because every unit you don't sell also saves its cost.
A single price is a compromise: set it high and you lose the thrifty, set it low and you give a discount to people who would have paid more. Price discrimination means charging different customers different prices for essentially the same thing, to collect more of each one's willingness to pay. It comes in three flavours: by person (student, senior, local-resident prices), by time or place (peak and off-peak, airport versus high street) and by version, where you offer a menu and let customers sort themselves. Economists tell the story, often credited to the nineteenth-century French engineer Jules Dupuit, of railways deliberately leaving third-class carriages uncomfortable, not out of cruelty or thrift but to keep well-off passengers from trading down. Whatever the history, the logic stands.
The menu version is the one you see every day: good, better, best. The trick is that the top version must be worth more to the high-value customer than the saving from the cheap one, or they will trade down. Economists call that the incentive constraint. The calculator below has two groups: 60 hobbyists who would pay $40 for a basic version or $50 for the pro, and 40 professionals who would pay $60 for basic or $120 for pro.
Each customer picks whichever option leaves them the most surplus, or nothing. Marginal cost zero (software). "One product" sells only the pro version. Illustrative groups.
The best single price (pro only, at $50) collects $5,000. With basic at $40 and pro at $100, the hobbyists buy basic, the professionals buy pro, and revenue is $6,400. Drag the pro price to $75: the professionals still buy pro, but you are charging them $25 less than they would pay, and revenue drops to $5,400. Drag it above $100 and they trade down to basic. Versioning works only where the customers truly differ in how much they value the extra.
Is it fair? Price discrimination is legal in most ordinary retail settings, and it can serve more people overall (the hobbyists get a version they can afford). It is restricted when it targets protected characteristics or in regulated markets such as utilities, and customers who discover they paid more for no visible reason tend to feel cheated. The honest firms hang the difference on something real: timing, quantity, features, or a cost.
Why does a streaming service sell hundreds of shows for one price, and a phone company a bundle of calls, data and texts? Because customers disagree about which parts they like. Take a software firm with two programs and two customers whose tastes are opposite: Ann values the writing program at $100 and the spreadsheet at $40; Ben values them at $40 and $100. Sold separately, each program's best price is $100 (one buyer) or $40 (two buyers: $80), so $100 per program and $200 in total. Sold as a bundle, both value it at $140, and one price of $140 collects $280. The bundle works because the high and low valuations cancel out and the customers look alike, which makes one price fit. Economists first described this in the 1960s and 1970s, with the Stigler (1963) film-licensing example and Adams and Yellen (1976).
| Customers (writer, sheets) | Separate, best | Bundle, best |
|---|---|---|
| Ann ($100, $40), Ben ($40, $100): opposite tastes | $200 | $280 |
| Ann ($100, $100), Ben ($40, $40): same tastes | $200 | $200 |
The second row is the warning. If the people who love one part also love the other, the bundle adds nothing. Bundling pays when valuations are negatively correlated or at least not strongly positive, and when the extra cost of giving each customer everything is near zero, as with digital goods.
Textbooks teach three price tricks with confidence. It is fair to ask how well each has survived testing, which is a theme of this whole series.
| Idea | Original claim | What the record shows |
|---|---|---|
| Charm prices ($9 endings) | $39 sells better than $40, even though 1 cent is 1 cent | Strongest of the three. Anderson and Simester (2003) ran three field experiments with a retailer and found 9-endings raised demand each time, more for new items and less when "Sale" cues were used. A large literature agrees on the direction; size varies with the product. |
| Anchors | An irrelevant number shifts what you'll pay: Tversky and Kahneman (1974); "coherent arbitrariness" (Ariely, Loewenstein and Prelec, 2003) | Anchoring in estimates is robust. The pricing version, that a random Social Security number shifts bids for wine and chocolate, was much weaker in later tests: Fudenberg, Levine and Maniadis (2012) found very weak effects for common goods and none for lotteries; other teams found small or null effects. |
| Decoys | A worse third option makes the target look better (Huber, Payne and Puto, 1982); popularised by a "web / print / print+web" magazine example | The most fragile. Frederick, Lee and Baskin (2014) reported that the effect largely vanishes with realistic products and descriptions. The famous magazine example comes from a classroom demonstration in a popular book, not a field test on the magazine's real customers. |
The lesson is not "psychology is fake". It is that the effects live in particular conditions and shrink in the wild, and that a price test on your own customers beats a story from a book. Test, and publish your own "lift" with its margin of error (see Marketing Research & Analytics, 34/59).
Illustrative split of 100 shoppers, not data. Add a medium size that is poor value next to the large, and suppose it nudges some people from small up to large.
Notice that the decoy only pays if the effect is real and big enough. At zero effect, the decoy just adds a pointless line to the menu. It is the numbers on the slider that would need testing.
An airline seat is perishable: at departure its value drops to zero. The airline has a fixed number of seats, a few business travellers who book late and pay a lot, and many holidaymakers who book early and pay little. If it fills the plane with cheap early bookings, the late business traveller finds no seat; if it holds seats back and they go empty, that is waste. The craft of deciding how many seats to protect for the high fare is revenue management, and it began in earnest when US airlines were deregulated in 1978 and low-cost rivals such as People Express arrived. In 1985 American Airlines responded with restricted "Ultimate Super Saver" fares, advance-purchase and non-refundable, sold only where it had empty seats; the case taught in business schools reports revenue up 14.5% and profit up 47.8% in the following year.
That rule is the heart of it. If the high fare is three times the low fare, protect seats until there's only a one-in-three chance of selling the next one at the high price. The calculator applies it to a 100-seat plane; with the starting settings the best answer is to protect 34 seats. Real systems handle dozens of fare classes, cancellations, connections and competitors, but they rest on this idea. Hotels, rental cars, concert tickets, ride apps with surge pricing and electricity time-of-use tariffs run on the same logic, with the same tension: the firm earns more, and customers feel the unpredictability.
100 seats; low-fare demand is large and books first; late high-fare demand is Normal with standard deviation 10. Revenue = low × (100 − protected) + 300 × E[min(demand, protected)]. Illustrative.
A subscription changes the question from "what will they pay today?" to "how long will they stay?". The value of a customer is roughly what they pay each month, times your margin, divided by the monthly churn (the share who leave): a customer who pays $10 at an 80% margin and leaves at 5% a month is worth about $8 ÷ 0.05 = $160 over their life. You can spend up to that much to win them, and a half-point of churn matters as much as a price rise.
Freemium gives a basic version away free and charges for more. It works when the free users cost almost nothing to serve, bring in others, or turn into payers at a rate that covers the rest. It fails when the free tier is generous enough that few ever need to pay, or expensive enough that they cost more than they bring. The calculator holds 1,000 free sign-ups and asks the plain question: does the paying minority cover everyone?
Paid gross margin 80%. Value of a payer = price × 80% ÷ churn. Illustrative.
A price is a choice of who you serve and how much of their gain you collect. Cost sets the floor, elasticity says how much volume each dollar costs, and versions, bundles and clocks let you charge different people differently. The psychology of price is real but smaller and shakier than the pop books say.
Try this: this week, spot one price menu (a coffee-cup sizes board, a streaming plan page) and work out which customer each option is built for, and which option is there only to make another look good.
Sources. Elasticity, the Lerner markup rule, Littlewood's rule (1972), bundling arithmetic and the LTV formula are standard microeconomics and revenue-management theory; every number in the interactives is computed in code from the stated assumptions and is illustrative, not data. Anderson and Simester, "Effects of $9 price endings on retail sales: evidence from field experiments", Quantitative Marketing and Economics 1(1), 2003. Fudenberg, Levine and Maniadis, "On the robustness of anchoring effects in WTP and WTA experiments", American Economic Journal: Microeconomics (2012). Frederick, Lee and Baskin, "The limits of attraction", Journal of Marketing Research 51(4), 2014. Huber, Payne and Puto, Journal of Consumer Research (1982). Tversky and Kahneman, "Judgment under uncertainty", Science (1974). Stigler, "United States v. Loew's Inc.: a note on block-booking" (1963); Adams and Yellen, "Commodity bundling and the burden of monopoly", QJE (1976). The American Airlines 1985 fare figures are as reported in the Harvard Business School case summarised on Wikipedia's Revenue management article; the Dupuit railway story is widely told and is given here as a story, not a verified quotation.