Water and Diamonds

It was during the nineteenth century – a time of relative peace and prosperity – that economics came into its own as a profession. In the hundred years between Napoleon’s defeat at Waterloo and the beginning of World War I, leading research universities began to establish economics departments separate in identity from moral and political philosophy. No longer was economics led by moral philosophers. In their place arrived men who were more interested in mathematics than moral philosophy, more likely to be versed in engineering than psychology. And this new breed of mathematically inclined economists revitalised the economic understanding of utility.

They would start by revisiting a conundrum identified by the founding father of their discipline: they would help explain, in a way Adam Smith had not foreseen, why diamonds are more valuable than water.

Adam Smith was not the first person to ponder the relative value of water and diamonds, but he is responsible for making the conundrum famous: "Nothing is more useful than water," he wrote, "but it will purchase scarce anything; scarce anything 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."

Smith understood value in two ways: the value in use of an object or its value in exchange. A hundred-dollar bill, by this distinction, has very little value in use. You can use it to help start a fire, or if you roll it up, I am told, you can use it to snort drugs. But the real value of a hundred-dollar bill is its value in exchange. You can trade it for hordes of useful things.

Water, for all its uses, is not so valuable in exchange, unless you happen to have an extra jug of it and come across a wealthy man lost in the desert. In normal situations, you cannot exchange a bucket of water for anything, because the person you are trading with can fill up his own bucket for free. Water’s value is all about value in use. You can drink it; water a plant with it; wash your clothes, your dishes, or your hair with it; and even fill a swimming pool with it.

So why doesn’t something with such great value in use have more value in exchange? Smith answered this question by tying the price of goods, their value in exchange, to the amount of labour it took to produce the good. If you want to know how much something costs, Smith suggests that you find out how much labour it took to produce it: "If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver than it does to kill a deer, one beaver should naturally exchange for or be worth two deer." Most early economists followed Smith’s lead, in attributing the exchange value of goods to the labour that produced them.

I expect many of you have noticed that something doesn’t seem right about Smith’s solution to the water/diamond conundrum. For by Smith’s logic, if it took the average hunter 20 hours to chase down and kill a squirrel and only an hour to shoot a deer, then people should be willing to trade twenty deer for one squirrel. That simply doesn’t jibe with common sense. For all his insight, Smith didn’t successfully isolate why diamonds had more value in exchange than water. The understanding came instead from someone who spent many hours intensely pondering the mysteries of water, a hydraulic engineer named Jules Dupuit.

Water under the bridge

Jules Dupuit was born in Fossano, Italy, in 1804, at a time when Napoleon still ruled much of Europe. When he was ten years old, his family moved to France, where the studious child who won numerous academic awards, grew up to become a studious young adult, graduating from the Ecole Polytechnic with a degree in civil engineering. After graduation, Dupuit remained in France, designing roads, bridges and water systems. In conducting this work, he thought deeply about the financial costs and benefits of these systems and how best to pay for them. What, for example, is the right toll to charge when people cross a public bridge? To answer this type of question, Dupuit taught himself economics.

Perhaps if he had been on the receiving end of formal economics lectures he would have been indoctrinated into the classical line of thinking. Maybe he would have become convinced that the value of a bridge depends on the labour that went into building it. But that logic didn’t make sense to Dupuit. If a bridge cost 100,000 francs to build, that still doesn’t tell us how much to charge any single person to cross the bridge. Even if your sole goal were to recoup the 100,000 franc investment, the correct toll would depend on how many people crossed the bridge, and the number of people who would cross the bridge would depend on your price of crossing.

What about the price of water from a public water system? Surely, you won’t try and recoup the cost of the system with the first cup of water. But how much should you charge for each cup of water? Here, Dupuit settled on the idea of marginal utility. Dupuit recognised that the value of water – its value in use – is not constant, but declines as more water becomes available.

Suppose, for example, that a hectoliter of water costs 50 francs. Dupuit concluded that every hectoliter of water consumed in these circumstances has a utility of at least 50 francs, because otherwise people wouldn’t purchase the water. But that doesn’t mean that every hectoliter is worth only 50 francs to people. In fact, the first hectoliter of water I buy at 50 francs will be very valuable to me, staving off dehydration. If water were scarce enough, I would gladly part with the better portion of my fortune to procure a hectoliter of water. The next hectoliter will still be valuable, but not quite as valuable. My immediate life will not depend on it. At some point, I will consider whether to buy another hectoliter of water, and decide that it is not worth 50 francs. That means the value of use of that first hectoliter (its utility) is not equal on average to the utility (or value in exchange) of 50 francs. Instead, it is the last bit of water I buy that is actually worth at least 50 francs to me.

Adam Smith was correct in writing that water often has tremendous value in use; fending off dehydration is a valuable thing. But lower the price of water enough, and people will use it for much less valuable things: lawn watering, car washing, and water balloon fights. To know the utility, then, of any consumer good, Dupuit directed people to look at the margins. If you look at how people use water when it is priced at 40 francs per hectoliter rather than 50, you’ll know which uses bring somewhere between 40 and 49 francs of utility per hectoliter. Dupuit’s insight would launch economists on a revolution in thinking know as the marginalist revolution.

Reprinted by permission of Harvard Business Press. Excerpt from Free Market Madness.  Copyright 2009 Peter A. Ubel. All rights reserve.