Paradox of value

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An image of water, a commodity that is essential to life. In the paradox of value, it is an apparent contradiction that it is cheaper than diamonds, despite diamonds not having such an importance to life.

The paradox of value (also known as the diamond–water paradox) is the apparent contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith is often considered to be the classic presenter of this paradox. Nicolaus Copernicus,[1] John Locke, John Law[2] and others had previously tried to explain the disparity.

Labor theory of value[edit]

Main article: Labor theory of value

In a passage of Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, he discusses the concepts of value in use and value in exchange, and notices how they tend to differ:

What are the rules which men naturally observe in exchanging them [goods] for money or for one another, I shall now proceed to examine. These rules determine what may be called the relative or exchangeable value of goods. 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; 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 scarcely anything; scarcely anything can be had in exchange for it. A diamond, on the contrary, has scarcely any use-value; but a very great quantity of other goods may frequently be had in exchange for it.[3]

Furthermore, he explained the value in exchange as being determined by labor:

The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it.[4]

Hence, Smith denied a necessary relationship between price and utility. Price on this view was related to a factor of production (namely, labor) and not to the point of view of the consumer.[5] The best practical example of this is saffron - the most expensive spice - here much of its value derives from both the low yield from growing it and the disproportionate amount of labor required to extract it. Proponents of the labor theory of value saw that as the resolution of the paradox.

The labor theory of value has lost popularity in mainstream economics and has been replaced by the theory of marginal utility.


At low levels of consumption, water has a much higher marginal utility than diamonds and thus is more valuable. People usually consume water at much higher levels than they do diamonds and thus the marginal utility and price of water are lower than that of diamonds.
Main article: Marginalism

The theory of marginal utility, which is based on the subjective theory of value, says that the price at which an object trades in the market is determined neither by how much labor was exerted in its production, as in the labor theory of value, nor on how useful it is on a whole ( ). Rather, its price is determined by its marginal utility. The marginal utility of a good is derived from its most important use to a person. So, if someone possesses a good, he will use it to satisfy some need or want. Which one? Naturally, the one that takes highest-priority. Eugen von Böhm-Bawerk illustrated this with the example of a farmer having five sacks of grain.[6]

With the first, he will make bread to survive. With the second, he will make more bread, in order to be strong enough to work. With the next, he will feed his farm animals. The next is used to make whisky, and the last one he feeds to the pigeons. If one of those bags is stolen, he will not reduce each of those activities by one-fifth; instead he will stop feeding the pigeons.

So the value of the fifth bag of grain is equal to the satisfaction he gets from feeding the pigeons. If he sells that bag and neglects the pigeons, his least productive use of the remaining grain is to make whisky, so the value of a fourth bag of grain is the value of his whisky. Only if he loses four bags of grain will he start eating less; that is the most productive use of his grain. The last bag of grain is worth his life.

In explaining the diamond-water paradox, marginalists explain that it is not the total usefulness of diamonds or water that matters, but the usefulness of each unit of water or diamonds. It is true that the total utility of water to people is tremendous, because they need it to survive. However, since water is in such large supply in the world, the marginal utility of water is low. In other words, each additional unit of water that becomes available can be applied to less urgent uses as more urgent uses for water are satisfied.

Therefore, any particular unit of water becomes worth less to people as the supply of water increases. On the other hand, diamonds are in much lower supply. They are of such low supply that the usefulness of one additional diamond is greater than the usefulness of one additional glass of water, which is in abundant supply. Thus, diamonds are worth more to people. Therefore, those who want diamonds are willing to pay a higher price for one diamond than for one glass of water, and sellers of diamonds ask a price for one diamond that is higher than for one glass of water.

Efficiency model[edit]

The Chinese economist Tan Lidong addresses the question through relative Economic efficiency. Noting that water is in such large supply in the world, but in the desert water-taking efficiency is very low, so the value of water is also high. If someone can invent high efficiency equipment to get water in the desert, by then the water would be cheap. He avers that value is determined by efficiency, as well as efficiency affected by tools, labor and resources.

He suggests we can calculate the exact value of the water or the diamond by using efficiency. He takes a historical approach to value, that exchange ratios have been known for many products for a very long time, and established by custom and practice. Technological change changes the efficiency of production, thus changing the relative values.[7]


George Stigler has argued that Smith's statement of the paradox is flawed, since it consisted of a comparison between heterogeneous goods, and such comparison would have required using the concept of marginal utility of income. And since this concept was not known in Smith's time, then the value in use and value in exchange judgement may be meaningless:

The paradox—that value in exchange may exceed or fall short of value in use—was, strictly speaking, a meaningless statement, for Smith had no basis (i.e., no concept of marginal utility of income or marginal price of utility) on which he could compare such heterogeneous quantities. On any reasonable interpretation, moreover, Smith's statement that value in use could be less than value in exchange was clearly a moral judgment, not shared by the possessors of diamonds. To avoid the incomparability of money and utility, one may interpret Smith to mean that the ratio of values of two commodities is not equal to the ratio of their total utilities. Or, alternatively, that the ratio of the prices of two commodities is not equal to the ratio of their total utilities; but this also requires an illegitimate selection of units: The price of what quantity of diamonds is to be compared with the price of one gallon of water?

George Stigler, The development of Utility Theory. I [8]

See also[edit]


  1. ^ Gordon, Scott (1991). "Chapter 7: The Scottish Enlightenment of the eighteenth century". History and Philosophy of Social Science: An Introduction. Routledge. p. 141. ISBN 0-415-09670-7. This 'paradox of value', as it was called, was frequently noted before Adam Smith (for example, by Copernicus who wrote a bit on economic questions)... 
  2. ^ Blaug, Mark (1962). "Chapter 2: Adam Smith". Economic Theory in Retrospect. Cambridge University Press. p. 39. ISBN 0-521-57701-2. Moreover, such writers as Locke, Law and Harris had contrasted the value of water with that of diamonds... 
  3. ^ Smith, Adam (1776). "Of the Origin and Use of Money". An Inquiry into the Nature and Causes of the Wealth of Nations. Retrieved April 2006. 
  4. ^ Smith, Adam (1776). "Book I, Chapter V Of the Real and Nominal Price of Commodities, or of their Price in Labour, and their Price in Money". An Inquiry into the Nature and Causes of the Wealth of Nations. Retrieved July 2006. 
  5. ^ Dhamee, Yousuf(1996?), Adam Smith and the division of labour accessed 09/08/06
  6. ^ Böhm-Bawerk, Eugen von (1891). "Book III, Chapter IV: The Marginal Utility". The Positive Theory of Capital. Retrieved 2006-06-20. A colonial farmer, whose log hut stands by itself in the primeval forest, far away from the busy haunts of men, has just harvested five sacks of corn... 
  7. ^ Tan Lidong <The economics of happiness>, publishing house of China university of politics and law (January 2012) ISBN 9787562040675
  8. ^ Stigler, George (1950). The development of Utility Theory. I. Journal of political economy 58(4), p 308.