The higher in carat weight the diamond is, the rarer and more expensive it will be per carat. This cost-price structure means that as we increase the carat weight, the price will increase exponentially.
For example:
(amounts do not necessarily represent the actual cost)
Carat x Price per carat = Total
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¼ carat x $1000 = $250
½ carat x $2000 = $1000
1 carat x $4000 = $4000
1 ½ carat x $6000 = $9000
2 carat x $8000 = $16000
As we can see, if we assume for simplicity, as above, that the price per carat increases proportionally to the carat weight, when we multiply the PPC by the carat weight, the total cost for the stone significantly increases as we go up the carat weight scale.