How can marginal utility explain the 'diamond/water paradox'?

One of the most disconcerting problems to Adam Smith, the father of modern economics, was he could not resolve the issue of valuation in human preferences. He described this problem in The Wealth of Nations by comparing the high value of a diamond, which is unessential to human life, to the low value of water, without which humans would die. He determined "value in use" was irrationally separated from "value in exchange." Smith's diamond/water paradox went unsolved until later economists combined two theories: subjective valuation and marginal utility.

Like nearly all economists of his age, Smith followed the labor theory of value. Labor theory stated the price of a good reflected the amount of labor and resources required to bring it to market. Smith believed diamonds were more expensive than water because they were more difficult to bring to market.

On the surface, this seems logical. Consider building a wooden chair. A lumberjack uses a saw to cut down a tree. The chair pieces are crafted by a carpenter. There is a cost for labor and tools. For this endeavor to be profitable, the chair must sell for more than these production costs. In other words, costs drive price.

But the labor theory suffers from many problems. The most pressing is it cannot explain prices of items with little or no labor. Suppose a perfectly clear diamond naturally developed in a perfect shape. It is then discovered by a man on a hike. Does it fetch a lower market price than an identical diamond arduously mined, cut and cleaned by human hands? Clearly not. A buyer does not care.

What economists discovered was costs do not drive price; it is exactly the opposite. Prices drive cost. This can be seen with a bottle of expensive French wine. The reason the wine is valuable is not because it comes from a valuable piece of land, is picked by high-paid workers or is chilled by an expensive machine. It is valuable because people really enjoy drinking good wine. People subjectively value the wine highly, which in turn makes the land it comes from valuable and makes it worthwhile to construct machines to chill the wine. Subjective prices drive costs.

Subjective value can show diamonds are more expensive than water because people subjectively value them more highly. However, it still cannot explain why diamonds should be valued more highly than an essential good such as water.

Three economists -- William Stanley Jevons, Carl Menger and Leon Walras -- discovered the answer almost simultaneously. They explained that economic decisions are made based on marginal benefit rather than total benefit.

In other words, consumers are not choosing between all of the diamonds in the world versus all of the water in the world. Clearly, water is more valuable. They are choosing between one additional diamond versus one additional unit of water. This principle is known as marginal utility.

A modern example of this dilemma is the pay gap between professional athletes and teachers. As a whole, all teachers are probably valued more highly than all athletes. Yet the marginal value of one extra NFL quarterback is much higher than the marginal value of one additional teacher. (For related reading, see: What does marginal utility tell us about consumer choice?)