Monthly Archives: February 2016

The Paradox of Value

After two centuries of development, economics still lacks a good understanding of how to value things. To be honest, I never realized the gaping hole in the field until recently, despite earning a Ph.D. in economics and teaching Econ 101 to hundreds of students over the years. Adam Smith mentions the “paradox of value” in the Wealth of Nations, but the idea was not original to him. Indeed, the diamond-water paradox was something Smith himself heard in lectures and can be traced back to the ancient Greeks, namely one of Plato’s earliest Socratic dialogues.

First, let’s review the diamond-water paradox, which is a staple of introductory econ lectures (indeed, I remember being fascinated by it as a college freshman, too). Why is a bucket filled with diamonds more valuable in monetary terms than a bucket filled with water? Water is necessary for life itself whereas diamonds are useless ornaments. Why does water cost so little and diamond cost so much?

The answer is that there are two different meanings of value, and that economics is dedicated to studying the monetary value of things. More accurately, the field of economics evolved to focus on market valuations, and as I have discovered, never resolved the other meaning. Adam Smith phrased it this way:

“The word VALUE, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called ‘value in use ;’ the other, ‘value in exchange.’ The things which have the greatest value in use have frequently little or no value in exchange; and on the contrary, those which have the greatest value in exchange have frequently little or no value in use. 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.”

A nice blog post on the diamond-water paradox by Timothy Taylor pointed me to a 2002 economic history paper by Michael White. White offers a nice history, but contends that it’s a myth that Smith could not resolve the paradox. This folklore emerged during the marginal revolution and was codified in Paul Samuelson’s 1948 textbook.

The standard lecture uses the paradox to highlight the radical power of market prices allocating resources through the power of supply and demand. Water is one of the most abundant substances, what with oceans covering two-thirds of the surface of the planet. This essentially endless supply makes water nearly free. Fresh water literally falls from the sky. Only in a dessert would a man dying of thirst (a locally constrained supply situation) be able to appreciate water’s great value. I don’t have a problem with Samuelson’s fable (in White’s words “Until 1871, the explanation for the discrepancy between the value in use and value in exchange remained a mystery because classical economists were incapable of resolving it.”) because to me the fable works in appreciating the explanatory power of the marginal analysis of utility, marginal cost, surplus, and all the rest. Sure, I accept that Smith understood the essence of the paradox. Smith understood that scarcity involved an interdependence of supply and demand, though he seems to denigrate conspicuous consumption of “baubles and trinkets.” Despite all this, I think everyone failed to resolve the deeper puzzle of cardinal utility and it remains unresolved by Smith as well as Marshall and Samuelson.

The second half of Smith’s explanation seems, to me, flawed still. Do you agree that things “which have the greatest value in exchange have frequently little or no value in use”? I don’t.

Diamonds in 1776 arguably had no industrial utility like today, but that’s not the point. Smith is defining “use” too narrowly. A century afterwards, economists engaged in a raging debate over the idea of utility, and the emerging consensus was that utility could not be quantified, but that pleasure and pain were important concepts that Smith neglected as a type of value. Recall the notion of ‘utils’ that you experience when consuming greater quantities of normal goods. Most understood utils to be useful as an explanatory device only. Other scholars believed further in a theory of cardinal utility, meaning that utils could be measured and quantified, but it seems that none could figure out how.

Despite that, we should not neglect Smith’s mixing up of use and utility. A diamond has sentimental value, or psychological value if you prefer, that is altogether distinct from its market value and its use value.

Here, I imagine I have lost most of my fellow economists. They are thinking of consumer surplus: the fact that a diamond consumer might purchase the item at a market price that is a fraction of what she would be willing to pay. The difference is what we call surplus, which some teachers (including me, back in the day) mistakenly call utility. But no, that surplus is itself a fraction of the satisfaction I mean to explain. Willingness to pay (WTP in the vernacular) is constrained by one’s budget, income, wealth, etc. However, unlike WTP, utility is not budget constrained. Consider the poor farmer girl whose fiance is a poor farmer boy; neither can afford a diamond ring now or ever. They are married, live, and die happily without ever owning a diamond or having any bearing on the demand curve for diamonds. Yet would this lass not value a diamond?

It is this sentimental sense of value that is not recognized by the market price (value in exchange) nor the demand curve’s surplus. It is a concept of value in utility – cardinal utility – that I want to understand. White reminds the reader that John Locke did establish this notion as “intrinsic” wants of mankind in the 17th century, and also that other 18th century scholars made the “use-exchange” distinction in books that Adam Smith had in his library. To repeat, Smith never claimed this insight to be original.

The Origins of the Paradox of Value

Thousands of years before Adam Smith was born, Plato wrote about the paradox of value in Euthydemus (Greek: Εὐθύδημος, Euthydemos), written around 384 BCE, one of his earlier Socratic dialogues. This history is delightful and, to me, just as important as what Plato actually wrote. As you may remember, the great philosopher Socrates never wrote any poems or books or anything at all. He is remembered only because his students, especially the brilliant Plato, wrote about him in their own plays and dialogues. This fact is an historical challenge exists – the Socratic Problem – about the impossibility of knowing “the ideas of the original Socrates as distinct from his literary representations.” A dominant view is that Plato’s earlier works are the truest homage, and that latter dialogues such as The Republic utilize the great man as a fictionalized character to represent Plato’s own ideas.

Euthydemus is a dialogue in which Socrates describes two rhetoricians, known as sophists, whose skillful and pugilistic wordplay is sarcastically praised. Socrates explains his long and playful conversation with the brothers to his friend, Crito. And after a lengthy description, finishes his tale by telling Crito that he (Socrates) expressed his admiration to the brothers but admonished them not show off their rhetorical skills to wide audiences, despite the acclaim and applause they often got. And here’s why:

“If you are wise, you will also bid your disciples discourse with no man but you and themselves. For only what is rare is valuable; and ‘water,’ which, as Pindar says, is the ‘best of all things,’ is also the cheapest.”

This is the advice of Socrates. the teacher, founder of the Academy where select groups of students paid to learn from his methods. What perfection! He says keep your discourses private among your disciples, for that will enhance the value of your words. Here we have Socrates not only touching on the value of scarcity, but explaining why he left no books. Books were not a source of revenue, in his view.

The passage begs the question, who was Pindar? He was famous in his time as a great lyric poet in Thebes. Pindar would have been an old man when Socrates was a young Athenian soldier. I have no idea if they met, but the passage indicates that Socrates had read Pindar’s famous first ode to the Olympics, which opens with the words, “Water is best” for survival, gold is best for wealth, in leading up to the glorification of victory in the games as best for one’s spirit.

Life, wealth, meaning.

Use, exchange, utility.

This may seem to be an esoteric issue, but take care to notice the many casual assumptions about value in newspaper and magazine stories. For example, the wry aside that teenagers “waste time” on Facebook which equals X million dollars per year. Time on books, social networks, video games, television, sports — these have no use but great utility. Notice the difficulty of measuring inequality in 2010 versus 1910. Notice how hard it is to measure inflation because consumption basket change dramatically. Notice how we talk about valuing public goods, national parks, and the environment. It’s a challenge. Finally, notice how government policy is distorted by assumptions that work and income should be taxed while uncompensated activity should not. Who produces value, after all?

The thread of value is woven into all things, and our search for its true meaning is far from over.