Price fencing: the fence that sorts your customers for you

You sell one thing. Your customers are not one thing.

The student with a side job and the procurement team of an insurer want the same product, but the amounts they consider reasonable are a factor of three apart. Set one price and you necessarily choose wrong. Too high, and the student leaves. Too low, and the insurer pays a fraction of what it was willing to pay. Most of the time you make both mistakes simultaneously.

Price fencing is the way out. You publish several prices side by side and put a fence between them: a condition that decides who may buy at which price. You don't decide which bracket someone belongs in. The customer decides, by meeting the condition or not.

A fence is not a discount, and the difference is the entire subject. Three properties make a condition a fence:

It is objective. Anyone can check whether you meet it. "Book 21 days ahead" is a fence. "You look like a wealthy customer" is not a fence, it's a guess.

It costs something. Whoever wants the low price gives up flexibility, convenience, features, or time. Without that sacrifice, everybody climbs over.

It correlates. The sacrifice has to weigh more heavily on those willing to pay more. A business traveller will not surrender their flexibility; a backpacker surrenders it cheerfully.

That third one is where fences earn their money, and it explains why you can't simply ask. Ask people what they'd pay and they answer strategically — low, because low is free. A fence asks nothing. It lets people reveal their willingness to pay by choosing, and choosing costs something, so lying gets expensive. Behaviour as testimony instead of words. (If you want to ask anyway, at least ask about edges rather than amounts — that's the Van Westendorp method, and it measures perception, not behaviour.)

The population behind every price

To see what a fence is worth, you first have to see what there is to collect. The figure above is a synthetic population: 4,000 prospects, each with their own maximum price — their willingness to pay. Consumers average €18.65 a month, businesses €58.13, and the whole population averages €30.49.

Two features of that shape do all the work later, and neither is an accident of this particular sample.

Two humps, not one. Each hump is a mechanism. Consumers pay out of their own pocket and compare against a cup of coffee. Businesses pay out of a budget and compare against an hour of an employee's time. Two unrelated ways of arriving at an amount, so two unrelated humps. Once you see a valley in the middle, that valley is your evidence that a fence can be built — and it tells you where.

Each hump leans right. The left side is hard-bounded: you cannot go below zero. The right side is open — there is always someone for whom money is not the issue. A bound on one side and freedom on the other always produces a skewed distribution with a long right tail (formally: lognormal). The consequence worth remembering is that the mean sits to the right of the peak, which makes the average willingness to pay a terrible candidate for your price.

From humps to a demand curve

Humps are pleasant, but you sell at prices, not at humps. So for each price p, convert them into a single question: what share of the population has a willingness to pay of at least p?

Q(p) = \Pr[\text{WTP} \ge p]

That's nothing more than stacking the humps up from right to left.

Two properties, again structural rather than behavioural.

It always falls — by construction, not by custom. Whoever buys at €40 has a willingness to pay of at least €40, and therefore automatically also belongs to the group "at least €30". Raising the price can only remove people from the group, never add them. A rising demand curve is not an interesting exception; it's an arithmetic error.

The kink in it is money. The steepness of the demand curve is the height of the hump beneath it. Where customers sit densely packed, every extra euro loses you many of them: steep. Between the two humps lies a valley, and there you lose almost nobody — that's the shoulder around €30. Price increases in the shoulder are nearly free; price increases on a hump are expensive. Which is exactly why your fence belongs in the shoulder.

What one price costs you

Now the part that stings. Set one price for everyone and the picture falls into three pieces. The convenient thing about these axes is that every area is an amount of money: a rectangle p wide and Q tall has area p \times Q, which is precisely revenue.

Every customer falls into exactly one of three categories, and together they fill the whole area under the curve:

• The rectangle — those who buy, and the part of their budget you actually capture: €1,112 per 100 prospects at the best single price of €19, where 58.5% buy.
• To the right of the rectangle — those who buy but would have paid more. They keep the difference: €1,382. That is not a mistake; that is the price of "one price for everybody".
• Above the rectangle, to the left — those you price away even though they were willing to pay something: €554.

The painful part is the arithmetic: the two loss regions together are larger than what you collect.

And you cannot close both. Slide the price to the right and the buyer's surplus shrinks — but the priced-away region grows. Slide it left and the reverse happens. One slider, two opposing leaks: you can move them, never seal both. That is exactly the problem a fence solves, because a fence is a second slider.

Why a wrong price feels so harmless

Plot revenue against every possible price — the area of that rectangle, for each p:

R(p) = p \times Q(p)

The hill is always a hill, never a line, because R(p) is a product of something that rises (p) and something that falls (Q). At low prices the rise wins: you double the price and lose almost nobody. At high prices the fall wins: one more tenner and half the market walks. Somewhere in between the balance of power flips, and that's the top — the point where elasticity is exactly -1, meaning one percent more price costs exactly one percent of customers. Left of the top the curve is steep; right of it, it trails off slowly, because that long tail of wealthy customers dies slowly.

The flat top is a trap, and worth being precise about why. Flat means revenue will not tell you that you're wrong. From €11.50 to €42.50 total revenue changes by less than 10% — while the composition of your customer base flips completely. And the whole hill, at every point on it, stays below 36.5% of the ceiling. You are optimising the shape of your compromise, not its height. To actually get higher you have to leave this chart, and the way out is a fence.

Two segments, two peaks

Split the revenue curve per segment and the compromise becomes visible.

The combined curve is a weighted sum of the two, and the weight is the number of customers. Consumers are 70% of the population, so their hump pulls hardest. The result: your single price lands on the big group and leaves the business hump virtually untouched. You serve the majority and subsidise the minority that needs it least.

Putting the fence in

Two prices means two rectangles nesting under the curve. Three prices, three rectangles. The staircase creeps toward the shape of the curve, and every euro between staircase and curve is money you previously left on the table.

Why a staircase and not a smooth curve? Because you only publish a handful of prices. Everyone in the same bracket pays the same, so within a bracket the line is flat: a tread. The curve is what you'd get with infinitely many fences — a personal price for every customer. So the staircase isn't an approximation of something complicated; the staircase is what you actually sell, and the curve is the upper bound you're climbing toward.

Where the treads land is not arbitrary either. A tread wants to be wide (high price) without losing much height (few customers lost), so treads settle on the shoulders of the curve, never on the steep parts. Notice that the top tread of the three-price version lands squarely on the business segment: the optimiser finds the fence you could already see with your eyes.

How many fences are enough?

There's an old and elegant result waiting here. For a straight demand curve, the optimal staircase with n prices captures exactly

\frac{n}{n+1}

of the theoretical ceiling. One price: half. Two: two thirds. Three: three quarters.

The curve flattens for a reason you can see in the staircase: each new fence slices off a strip between staircase and curve. The first fence gets to pick the thickest strip, the second gets what's left, and so on — the strips get inevitably thinner. That's the whole source of the concavity. Practically: at three brackets you have 66.7% in hand, and every bracket after that costs you explanation, choice paralysis and support time for steadily less money. Which is why good–better–best is so stubbornly popular. That is precisely where the gains stop being interesting.

One more thing about that chart deserves attention, because it's the strongest argument in the whole piece. Our curve starts below the textbook line: 36.5% instead of 50%. The n/(n+1) rule assumes a straight demand curve, where customers are spread evenly. Our population is humped, so one price must choose one hump and abandons the other entirely — hence the underperformance. But that is exactly what makes the first fence so lucrative: it picks up the hump you were abandoning. The more unequal your customers, the worse one price does, and the more a fence is worth.

What fences are made of

A fence is a condition that is (a) objective, (b) costly, and (c) more costly for those willing to pay more. That leaves a surprising amount of building material.

kind of fence	what it looks like	why it works
time ahead	Early-bird tickets, advance-purchase fares, annual prepay.	Whoever books late books because they must. Urgency and willingness to pay move together.
time of use	Off-peak fares, weekend rates, happy hour, night tariffs.	Whoever has to be there at the peak moment has a reason worth money.
stay & shape	Saturday-night stay required, return instead of one-way, non-refundable.	The classic airline fence: the business traveller wants to be home on Saturday, the tourist doesn't.
quantity	Volume discounts, bundles, season tickets, ten-trip cards.	Buying ahead costs liquidity and trust — the intensive user has both.
execution	Good–better–best, SSO and audit logs only in the top tier.	The fence is the feature list. Whoever needs the feature has the budget.
identity	Student, youth, senior, non-profit rates.	Verifiable with a document, strongly correlated with budget, and it feels fair.
channel	Factory outlet, foreign edition, marketplace listing.	Going somewhere else costs time and convenience — exactly what the hurried customer won't spend.
effort	Clipping a code, filing for cashback, waiting lists, blind booking.	A pure effort fence: identical product, just more cumbersome. Those with time to spare usually have less money to spare.

The distinction that matters: a discount is a lower price. A fence is a lower price with a condition that costs the customer something. Remove the condition and you no longer have fencing — you have a price cut for anyone who asks. Which is precisely what happens to a coupon code that ends up on an aggregator site.

When the fence leaks

Fences leak. The code lands on a coupon site, the company lets an employee pay "as a private individual", the business traveller turns out to be perfectly able to skip a Saturday. So the question isn't whether it leaks, but how much leakage you can tolerate.

First, measure the right thing. The leakage rate is not "how many customers take the discount" — hopefully that's plenty, that's the point. It is: how many of the discount customers would have paid full price. You don't read that off your invoices; you get it from a difference. Roll the fence out in half your market, keep the other half on one price, and compare average revenue per customer. What you lose in full-price buyers is visible only against a control group.

Take the two-price setup — €42.50 and €14 — and let a share of the full-price payers climb over the fence to grab the low rate anyway.

Both lines are dead straight, and that's genuinely useful. Every customer who climbs over costs you exactly the same amount: €42.50 − €14 = €28.50. Not more for the tenth climber than for the first. A constant cost per unit of damage gives a straight line — no acceleration, no tipping point, no disaster that suddenly announces itself. Which means you can plan with a single number: the slope is €6.74 per percentage point of leakage, per 100 prospects.

The deep-discount line breaks much earlier, and it does so for two reasons at once. It starts lower (you earn less from the group that legitimately deserves the discount) and it falls more steeply (every climber costs more). Hence the rule: the deeper the discount behind the fence, the more watertight the fence must be. A rate 20% below full price may rattle a bit; a rate 80% below has to be verified.

There's a lesson hiding in why that first break-even is so absurdly forgiving. 96% leakage sounds impossible to reach — and the reason is that the low rate, €14, is a perfectly sensible price on its own, close to the flat top of the revenue hill. Whoever climbs over falls back onto something you'd nearly have charged anyway. So: a fence whose both rates are defensible is robust. A fence with a gift behind it is fragile.

What goes wrong in practice

• The fence feels arbitrary. Customers accept fences they can retell: student, volume, book early. They do not accept a fence they can't see or can't follow. A price that varies by your device or your postcode produces an angry thread, not revenue.
• The fence is a guess, not a fence. Personalised prices based on behavioural data are legally and reputationally fraught, and they miss the point entirely: the customer is supposed to sort themselves. Let the condition do the work.
• Cannibalisation unmeasured. The only number that matters is how many customers who would have paid full price now pay the low rate. Measure it before you roll the fence out and again afterwards. The leakage chart is useless without that percentage.
• Too many brackets. After three or four brackets the gains are thin. The costs — explanation, hesitation, support, migration pain — are not. More tiers feels thorough and computes badly.

What to carry away

Your customers differ in willingness to pay, and that distribution has humps, not an average. The mean sits to the right of the peak and describes nobody.

One price captures about a third of what's there — 36.5% here — and leaves two kinds of money behind that you cannot recover simultaneously.

A fence is a second slider: an objective condition that costs effort, and more effort for those willing to pay more.

The first fence is the big one. It's worth 21 points here; after that the returns flatten fast, and three brackets is nearly always enough.

Flat revenue hides your mistake. Across a fourfold price range, revenue moves less than 10% while your customer mix inverts completely. Don't take a stable top line as evidence the price is right.

Leakage is linear, and therefore predictable. One number — the price gap times the number of climbers — tells you the whole cost. The deeper the discount behind the fence, the tighter the fence has to be.

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The figures here come from a synthetic population of 4,000 prospects: two lognormal willingness-to-pay distributions, 70% consumers around €17 and 30% businesses around €54. Price staircases are exact optima computed by dynamic programming over a half-euro grid, so the amounts are internally consistent — but no real market was measured. The shapes and proportions are what matter, not the cents.