With the whole note you buy less than with loose change

Eighty-nine undergraduates filled in a questionnaire at two universities in the United States and were paid a dollar for doing it. Forty-three were paid with four twenty-five-cent coins; forty-six, with a one-dollar bill. Then all of them were offered the sweets from the campus cafeteria: a packet of gum priced at exactly that dollar, with cheaper and dearer things beside it.

Among those carrying the four coins, sixty-three per cent bought. Among those carrying the bill, twenty-six.

The same dollar and the same counter: two and a half times as many purchases in the group that was carrying it loose.

That is what happens to you on Monday, when you break a fifty to pay for the shopping and by Thursday there is nothing left and you cannot say where it went. Format decides: the same amount, in one big piece, gets spent less than it does split into small ones.

It was measured by Priya Raghubir, of New York University, and Joydeep Srivastava, then at the University of Maryland, and published in December 2009 in the Journal of Consumer Research, the academic journal where research on buying decisions appears. The paper is called, literally, "the denomination effect": denomination is the value printed on each note or coin.

They repeated it off campus, which is where this sort of thing usually falls apart. At a petrol station they approached seventy-five customers and paid them five dollars for answering a survey: some with five one-dollar bills, some with five one-dollar coins and some with a single five-dollar bill. Those who got the five small bills were the ones who bought most in the shop: twenty-four per cent. Those with the five-dollar bill, sixteen. Those with the coins, twelve.

And they repeated it in China, with a hundred and fifty women aged between twenty-five and forty-five. It was not done in the street: an agency recruits them and takes them one by one into a room, and there they are handed an envelope with a hundred yuan either as a single note or split into five. The ones who received the single note ended up less satisfied with the household things they bought with it.

There is a detail there that spoils the easy version of the story, and it is what makes the rest trustworthy. If the rule were "the smaller the piece, the more you spend", the people carrying five one-dollar coins should have bought more than anyone, and they bought the least of the three groups. The dollar coin barely circulates in the United States: there are people who have never held one. A rare object is not treated as change; it gets kept. What decides this is how much it costs you to part with the piece you are carrying.

The mechanism, without the jargon: a large note is a whole piece, and breaking a whole piece costs something. Loose change is already broken. The authors sum it up like this: the big piece feels like an object you own, and loose change like an amount you use. That is why the whole note gets defended and the coin does not, although they are worth the same and sit in the same pocket. There are grandmothers who have spent half a century saying "don't break the fifty" without having read anyone.

It is worth saying how far this goes, because in this field plenty of famous results have collapsed when somebody repeated them. Nobody has demonstrated that a big note will fix your month, and nobody has ever compared a fifty-euro note with five tens: what was compared was a whole dollar against four coins, five dollars against five singles and a hundred yuan against five notes. And be careful about dismissing those sums as small. A dollar and five dollars are; a hundred yuan is not. Two thirds of those hundred and fifty women earned between three hundred and six hundred yuan a month, and nearly one in five less than three hundred: a hundred yuan was at the very least a sixth of their pay, and for many of them more than a third. The effect held just the same. What travels from there to your wallet is the direction of the effect, and nothing else.

With a card there is no piece to break, and that the experiment did not measure.

So tomorrow, when you take cash out, ask for it in the largest note the machine will give you — in euros that is the fifty — and do not change it until you have no choice.