Why does a diamond cost more than water?

Water keeps you alive. Go three days without it and you die. A diamond does nothing for you at all. And yet a small stone can cost more than all the water you will drink in your life.

Adam Smith put the puzzle in plain words in 1776, in The Wealth of Nations: “Nothing is more useful than water: but it will purchase scarce any thing; scarce any thing can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.”

He was not the first to notice. John Law, the Scottish financier, had used the same pair of examples in 1705. But Smith, the most influential economist of his age, could not solve it. He settled for splitting value in two: value in use, which water has plenty of, and value in exchange, which diamonds have. That gives the problem a name. It does not explain it.

For the next hundred years, the leading theory said that things are worth the work it takes to make them. That helps a little with diamonds, which are hard to find and to cut. But it falls apart quickly. A pearl found by luck on a beach is not worth less than one brought up with great effort. A painting is not expensive because it took a long time to paint. And a bucket of water carried up a hill does not become a luxury.

The answer: the next one

In the early 1870s, three economists in three countries, who had never met, reached the same answer within a few years of each other: William Stanley Jevons in England, Carl Menger in Austria and Léon Walras in Switzerland.

Their insight was that nobody chooses between all the water in the world and all the diamonds in the world. We choose one more unit, starting from what we already have. And what one more unit is worth to us depends on how many we already have.

Think of the cups of coffee in your day. The first one in the morning is worth a lot to you. The second, less. By the fifth you might pay someone to take it away. The coffee is the same; what changes is where it falls in your day. Economists call this marginal utility: the value of the last unit, not of the whole.

Water is everywhere, so almost all of us are at the fifth cup. One more liter adds almost nothing, and its price is low, even though water as a whole is priceless. Diamonds are scarce, so for almost everyone one more diamond would be the first. Its price is high, even though diamonds as a whole matter very little.

The paradox disappears. Price does not measure how important a thing is. It measures how much the next unit is worth, given how many there are.

Two tests of the idea

The theory makes two predictions, and both can be checked.

If water becomes scarce, it should become expensive, however ordinary it is. That is what happens in a drought, a siege or a desert, where people have paid a fortune for a single drink.

If diamonds become plentiful, they should become cheap, however beautiful they are. That is happening now. Diamonds grown in laboratories are chemically identical to mined ones, and as factories have turned out more of them, their price has fallen to a fraction of what a mined stone costs.

Why it mattered

The answer to a riddle about water and diamonds changed economics. If value depends on how people value the next unit, and not only on the work put in, then prices are signals about scarcity and about what people want. That idea sits behind supply and demand curves, behind how firms decide how much to produce, and behind a large part of the economics taught today.

It also undermined the labor theory of value on which Karl Marx had built his idea of exploitation. Not everyone accepted that, and the argument has never quite ended.

Ideas, the fourth book of Everything Has a Price, tells how the marginal revolution happened, how three men reached the same answer by three different roads, and what it did to the debates that followed.