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Very large emeralds (over 10 cts) of good quality are extremely rare. Most of them are in museums, crown jewels or the jewelry boxes of the elite. Emeralds over 3 cts are even rare, available to average people for thousands of dollars. An emerald of good quality of any size is valuable, though the price will go down significantly when the stone is less than 1/2 carat.
In the wholesale gem trade, emeralds are sold on a price per carat basis. Therefore, it would make sense that a 3 carat emerald would cost more than a 1 carat emerald, all else being equal. However, an aditional factor is that it is rarer to find a 3 carat emerald than a 1 carat emerald. Therefore, not only is the total price higher, but the price per carat is also higher because of the added rarity factor.For example, a 1 carat emerald of excellent quality might cost $1000. A 3 carat emerald of the same quality would NOT cost $3000 (3 X 1), rather it might cost $8000.