Cross-border shopping trips

Why does a small price gap across a border move whole busloads of shoppers?

A packet of coffee costs three euro on one side of a line and two-forty on the other. One euro of duty separates a litre of spirits. Nobody would cross a road for that, let alone spend a Saturday on a coach.

And yet the coaches run. Car parks on the cheaper side fill with foreign plates, whole retail parks exist within sight of the crossing and nowhere else, and a tax change of a few percentage points can empty or fill them within a month. Something turns a difference too small to notice into a movement large enough to see from the air. What?

Let us be precise about what is small. The gap is small per unit. But nobody crosses a border for one packet of coffee, so the per-unit figure is the wrong thing to compare against the cost of the trip.

Do the arithmetic instead. Say the trip costs twenty-five euro all in — fuel, the coach seat, the wear of an afternoon. The coffee saves sixty cents a packet. Two packets save one-twenty, which is absurd against twenty-five. Twenty packets save twelve euro, still a loss. Fifty packets save thirty, and now the trip is worth making. The saving scales with what you carry; the cost of the trip does not.

That already tells us the shape of the thing. The trip cost is a fixed toll to be paid before any gain arrives, so nothing happens at all across a wide range of gaps — and then, past a threshold, everything happens. There is no gentle response to a small differential, because the fixed cost has to be cleared first. That is why the reaction looks so disproportionate to the gap that caused it.

Now ask a second question: why a border, particularly? Prices vary continuously across any country, after all. But they vary gently, over hundreds of kilometres, so the gain from driving one town further is roughly cancelled by the cost of driving there. A border is not a slope. It is a step: the excise regime, the value-added rate and the currency all change within a few metres. The entire differential is available for one crossing, at the lowest possible travel cost. That is what makes a border special — not that the difference is large, but that it is concentrated.

So the flow depends on a differential and a distance, and it will be strongest exactly where the two are most favourable. Follow that out and it predicts the geography: shopping intensity should be extreme in the first few kilometres and fall away sharply inland, since every kilometre of travel eats saving without adding any. That is what the retail parks pressed up against crossings are — the flow made visible where it is densest.

Ask next which goods move, because it is not everything. What matters is saving per unit of car boot: a good needs a large gap relative to its bulk, and it must survive the journey. Alcohol, tobacco and fuel qualify on all counts, since their prices are mostly tax levied per unit. Groceries qualify weakly, in bulk. A restaurant meal cannot cross at all. Fuel is the cleanest case, since the tank must be filled anyway and a detour costs almost nothing.

One more thing to notice, because it explains the speed of the changes. The gradient is not stable. An excise increase moves it overnight; so does an exchange rate, which is why sterling weakening or strengthening flips the direction of traffic across the Irish border within weeks, in both directions at different times. And the response is fast in one direction and slow in the other: shoppers stop coming immediately when the gap closes, but the shops built for them do not un-build, so a border town can be left with retail capacity sized for a flow that has gone.

Finally, the flow acts back on what drives it. Every crossing shifts tax revenue from one treasury to the other, so the losing government eventually reacts — cutting its rate, capping allowances, or tightening enforcement. The differential creates a pressure to reduce itself, which is why neighbouring states' excise rates track each other more closely than their politics would suggest.

The most common misreading is that the shoppers are behaving oddly — driving two hours to save "a few euro". They are not saving a few euro. They are saving a few euro per unit across a basket sized deliberately to clear the trip cost, which is why boots come back full and why allowance limits, rather than prices, are what actually bound the trade.

Second, it is worth separating the gradient from the flow. The differential is a standing condition, set by tax and exchange rates. The flow is what it produces given the resistance in the way — distance, time, queues at the crossing, customs allowances, the bother of it. Both terms matter, and policy usually acts on the second because the first is politically expensive: a slow border does as much to stop the traffic as a tax cut would, at no cost to revenue.

One honest limit. The threshold reasoning assumes shoppers weigh the trip against the saving, and some of the traffic is plainly an outing that would have happened anyway, with the saving as justification rather than cause. The arithmetic explains the pattern well without requiring that every passenger did the sum.

• How customs personal allowances, rather than prices, become the real limit on the trade.
• Why fuel is the extreme case, and what that implies for filling stations near borders.
• Whether tax competition between neighbouring states converges rates, and how far the effect reaches inland.

Every term the collection defines is gathered in the glossary.