‘Diamonds are costly because we desire them. But what if that isn’t true? What if they are desirable because they are costly?’

A glass of water costs very little; a diamond costs a lot. Yet there is nothing more useful than water, while the most prized uses of diamonds are decorative. This apparent paradox has tested some fine minds. Adam Smith’s answer to the paradox was that diamonds were expensive because it was hard work to find them and dig them up. That seems to strike close to the truth but it’s not the way that modern economics approaches the problem.

The usual name for this puzzle is the “paradox of value” or “the water-diamond” paradox but I now prefer to call it the “Button Gwinnett paradox”. (I hadn’t heard of Button Gwinnett until his life was described in a recent episode of the WNYC radio programme Radiolab.) The British-born Gwinnett moved to the colony of Georgia in the mid-1700s. He was a failed businessman, a serial debtor and a B-list politician in the independence movement. But, as it happened, he was one of the 56 signatories of the Declaration of Independence.

Gwinnett might seem a minor figure compared to some of the other men whose names sit beside his: John Hancock, Thomas Jefferson, John Adams and Benjamin Franklin. Despite that, a Button Gwinnett signature is vastly more valuable than a Jefferson or a Franklin. The simple reason for this is that collectors naturally wish to own the complete set of 56 signatures. Ben Franklin lived into his eighties and was a prolific correspondent, so there is no shortage of Franklin signatures.

Gwinnett died in a duel the year after signing the Declaration of Independence. His signature was recently discovered on the parish register of St Peter’s Church in Wolverhampton, where he was married. Most of the other signatures he left behind were on IOUs.

Benjamin Franklin may have been one of the most remarkable human beings in history but when collecting your set of Independence signatures, it’s the Button Gwinnett that will prove the final piece of the jigsaw. Anyone selling a Gwinnett will find few other sellers and many eager buyers.

Which brings us back to water and diamonds. Diamonds are expensive because at the point at which the supply of diamonds dries up, there are plenty of buyers willing to pay handsomely, and they compete with each other. Water is cheap in temperate climes because after satisfying our demand for drinking and cooking, then for washing and for irrigation, and finally for swimming around in, there is still plenty left. The value of the first litres of water may be incalculably high but the marginal value of one more litre is very low, and it’s this value that sets the price.

Everything so far has assumed that our desire for an object — a diamond, a glass of water, a Button Gwinnett signature — is a given. Diamonds are costly because we desire them, and not the other way around. But what if that isn’t true? What if diamonds are desirable because they are costly?

The economist Thorstein Veblen coined the term “conspicuous consumption” to describe situations where an object is attractive merely because it is expensive. The designer watch or car is valuable because, like a peacock’s tail, it is a credible indicator that you have resources to spare. What was the point of spending so much on that diamond engagement ring otherwise?

Another possibility is “pricing bias”. If we don’t really know a good suit or a good bottle of wine from a bad one, we tend to use the price to give us a clue. This is not strictly logical — after all, anyone can double the asking price of anything they are selling, so price is not by itself a reliable clue to quality. But pricing bias exists. Studies show that people will rate a wine more highly in a taste test if they think it is expensive; even placebo painkillers are more effective if the patients believe they are costly new drugs rather than cheap new drugs.

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The final word on this should go to a team led by Laurie Santos at Yale’s Comparative Cognition Laboratory. Santos has spent some time teaching capuchin monkeys how to use money, to exchange it for food and to understand the idea that food can have a price that is high or low. In recent work with Robin Goldstein of UC Davis, Santos’s team has been trying to figure out whether the monkeys also display pricing bias.

It seems not. After a series of trials where monkeys were allowed to buy cheap or expensive jelly and ice lollies, they were then let loose on a free buffet to see if they gravitated towards the once costly items. They didn’t; unlike humans, the monkeys couldn’t care less what the item typically cost. They liked what they liked. In this, they differ not only from humans but also from starlings: Alex Kacelnik and Barnaby Marsh, zoologists at Oxford, have found that starlings prefer more costly food.

My guess is that the monkeys would have little interest in a Button Gwinnett signature. And those glossy advertisements for diamonds and designer handbags? They are evidently far too sophisticated for capuchin tastes.

Written for and first published at ft.com.