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Is the value listed for a gem its buying price, selling price, or something else?

Gems are listed with a value in the DM Guide as treasure. In this context, it would imply the gem could be sold for that number of gold pieces.

Gems worth particular amounts are also mentioned in the Player’s Handbook as material components for spells, where one might assume that is the (approximate) price in gold pieces to buy the specified gems.

Example:

Imagine a wizard finds a 40 GP diamond among some treasure. He sells it to a gem merchant and then buys a 50 GP diamond to use as a material component. (Our honest gem merchant needs to charge a reasonable margin to stay in business.) The wizard checks out his new purchase — could he be looking at the same darn diamond?

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The Player's Handbook and basic rules both say this under "Selling Treasure" in chapter 5:

Gems, Jewelry, and Art Objects. These items retain their full value in the marketplace, and you can either trade them in for coin or use them as currency for other transactions. For exceptionally valuable treasures, the DM might require you to find a buyer in a large town or larger community first.

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Gems are considered a trade good and thus you can buy and sell them at the given price.

This is location in Chapter 7 of the DMG on 133. Page 134 starts listing the different Gems that can appear in a given price range. I do not have any web links.

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