In a word, scarcity. Diamond is scarce so it has a high price. Water is not so scarce.

There are always two sides to a market, demand and supply. There is actually a lot of demand for water in most societies. However, water is cheap where it is plentiful. But suppose that water is scarce in some places, it could be expensive there. Diamonds are expensive because they are scarce. But suppose that the demand for diamonds were tiny, because people no longer wanted to decorate their bodies with the damn things. Well then, diamonds would become relatively cheap. So the paradox to which you refer is the result of typical demand and supply characteristics and not some imutable law.

the diamond/water paradox that perplexed Adam Smith became more understandable after marginal utilities are considered.

I subscribe to the hint provided by Rob. If decisions would be based only on total utility of the two goods, we can simply asses that, biologically, water is more important for life than diamonds, thus the total utility of water is bigger than the total utility of diamonds. However, thinking in marginal terms is more realistic: the marginal utility of water, which is the extra satisfaction than we obtain for consuming one more unit of water, is, in general, lower than the marginal utility of diamonds.

The role of demand has been already commented upon. I would point out the role of cost. Whatever the level of demand for a certain good, equilibrium price can never be lower than its average cost. It happens that the average cost of daimonds is incomparably higher than the average cost of (even drinking) water. Moreover, while the supply curve of diamonds can be supposed to be upward sloping, water supply curve in many regions is likely to be almost flat for the relevanti interval.

The classical solution to this paradox you may find in Carl Menger's "Principles of Economics" (1871):

If we ask, for example, why a pound of drinking water has no

value whatsoever to us under ordinary circumstances, while a

minute fraction of a pound of gold or diamonds generally exhibits

a very high value, the answer is as follows: Diamonds and gold are

so rare that all the diamonds available to mankind could be kept in

a chest and all the gold in a single large room, as a simple calculation

will show. Drinking water, on the other hand, is found in such

large quantities on the earth that a reservoir can hardly be imagined

large enough to hold it all. Accordingly, men are able to satisfy

only the most important needs that gold and diamonds serve

to satisfy, while they are usually in a position not only to satisfy

their needs for drinking water fully but, in addition, also to let

large quantities of it escape unused, since they are unable to use up

the whole available quantity. Under ordinary circumstances, therefore,

no human need would have to remain unsatisfied if men

were unable to command some particular quantity of drinking

water. With gold and diamonds, on the other hand, even the least

significant satisfactions assured by the total quantity available still

have a relatively high importance to economizing men. Thus concrete

quantities of drinking water usually have no value to economizing

men but concrete quantities of gold and diamonds a high

value.

In the Ludwig von Mises Institute's edition (downloadable from here: https://mises.org/system/tdf/Principles%20of%20Economics_5.pdf?file=1&type=document)

it's on page 140.

@Rob Catlett @Andrea Salanti

The story that "diamond/water paradox" perplexed Adam Smith (Rob Catlett) is an urban legend that was created by the neoclassical economics, or present-day main stream economics. Smith wrote on the example of water and diamond in his Wealth of Nations, Book I, Chapter 4, paragraph 13:

• 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.

Smith wrote this paragraph in order to explain how the exchange values are regulated in the subsequent chapters of Book I (mainly in chapter 5). The diamond/water parable is no enigma or paradox for Smith. This was posed only to attract interest from his readers for subsequent chapters. Smith knew the answer very well.

His answer was simple. It is something similar to Andrea Salanti's. Simply stated, it dues to a large difference of amount of labor that is necessary to obtain a diamond and a bucket of water. In the history of economics, this theory is called labor theory of value. This theory had some deficiencies and it was improved by David Ricardo into cost-of-production theory of value. The modern form of Ricardo's theory is explained for example in my paper:

Shiozawa (2015) The Revival of Classical Theory of Values.

https://www.researchgate.net/publication/269393496_The_Revival_of_Classical_Theory_of_Values

The urban legend was created by founding fathers of the neoclassical school, including Stanley Jevons and Carl Menger. Jevons argued diamond and water example in three paragraphs in his book The Theory of Political Economy. In Chapter 4, paragraph 7, he even cited the above paragraph of Smith as a whole.

Jevons wanted to show that the exchange value of commodities is proportional to their marginal utility (this term is due to Menger. Jevons used the expression "final degree of utility"). He used the water and diamond parable in order to compare the total utility theory of value with the marginal utility theory of value. The parable becomes paradox only when we think that the value of a commodity must reflect the strength of its utility.

The deeper question is: which of the value theories is better as a price theory of modern industrial economy? When two people meat with water and a diamond in a desert and negotiate the terms of trade, the neoclassical theory, or the marginal utility theory of value, holds. In a modern industrial economy, where most commodities can be produced without limit at almost constant cost, the cost-of-production theory is much more plausible than the marginal utility theory.

Let me add as a final remark that values of financial instruments are not determined by none of above two value theories.

Adam Smith noted that, even though life cannot exist without water and can easily exist without diamonds, diamonds are, pound for pound, vastly more valuable than water. The marginal-utility theory of value resolves the paradox. Water in total is much more valuable than diamonds in total because the first few units of water are necessary for life itself. But, because water is plentiful and diamonds are scarce, the marginal value of a pound of diamonds exceeds the marginal value of a pound of water. The idea that value derives from utility contradicted Karl Marx’s labour theory of value, which held that an item’s value derives from the labour used to produce it and not from its ability to satisfy human wants.

dear Ms. sarika

thank you for your valuable response.

can you please elaborate on Karl Marx’s labour theory of value

Mrs Sarika Rajesh Patel and Dr Srikanth Potharla

Have you read my post a month ago? I have explained all those stories. It is not Karl Marx who started the labor theory of value. Adam Smith had it. You two are confused by the later apologetic fake news.

thank you prof. Yoshinori for guiding me in understanding the genesis of Labour theory of value.

I do not know the historical perspectives of Economic theories.

thanks a lot for providing right historical perspective of theory of value.

Hi Peter F. Colwell can you explain the diamond water paradox using demand and supply graphs?

Yes . . . and so can a great many others. Google it.