Wednesday, January 20, 2010

Diamonds and Water

For the sake of economic literacy, here's a classic paradox in economics (I borrowed the phrasing from here)

Adam Smith presented the diamonds and water paradox in The Wealth of Nations in 1776:
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.
Just like Smith, ordinary people still puzzle over why goods we could do without fetch high prices, but some goods with high “value in use” sell for much less than they are worth. We can resolve this paradox by recognizing that price is independent of value. To see why this is the case, consider an example. If you value a red trenchcoat at $50, that means that the maximum you were willing to pay for the trenchcoat is $50 by our definition of value.

• If the price of the coat is $60, the maximum you are willing to pay for the coat is still $50, so you don't buy the coat.

• If the price of the coat is $40, the maximum you are willing to pay for the coat is still $50, even though you actually paid less.

• Taken further, if someone gives you the coat, the maximum amount you were willing to pay for the coat remains at $50. You're just really happy because you got a coat worth $50 for nothing.

Given this backdrop, the only thing we know that relates price of a good to its value is that, in voluntary markets, consumers willingly decide to pay the market price for the good. In this case, the equilibrium price of a product reflects the maximum amount that some marginal consumer would willingly pay for the last traded unit of the good. The price tells us nothing about the value of the other units traded in the market except that their value exceeds the price. Importantly, the price tells us very little about the total value of the good to consumers of that good.

Much more water is traded than diamonds because water is abundant, but diamonds are scarce. Diamonds command a higher price because they are rare, but the total value of water likely exceeds the total value of diamonds -- just think of which you would rather do without for a week.

The paradox applies to more than just diamonds and water. For example, some propose that people in some professions don't get paid enough, whereas others get paid a lot for putting a ball in a hole or basket. My answer is that the former are like water (valuable and abundant), and the latter are like diamonds (their skills are rare).

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