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In 5e, magic items aren't as common or as varied as in older editions, but that also means it is hard to place prices on them.

As DM, NPC's can't really sell a magic item because we don't know the prices for these items. While it is stated that they are rare and usually unpurchasable and unsellable, but I still have to have some basis on what to price them.

So is there a way to find buying and selling prices for magic items in 5e?

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On page 133 of the Dungeon Master's Guide, there is a table labelled Magic Item Rarity which gives a rough guidelines on the value of magical items, from Common rarity (for 50gp upwards) through to Legendary rarity (for 50,000gp or more).

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Canon RAW answer is that the DMG gives some orientative guidelines, as @Tashio mentioned.

Some players think that the rarity classification leaves much to be desired, however; Giant in the Playground user Saidoro wrote the article Sane Magic Item Prices to address the problem, you might want to check it out and adapt it to your own needs.

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    \$\begingroup\$ Just as a warning to those following this advice: Sane Magic Item Prices is a GREAT resource! But :-). While it works well for selling prices, it does not account for the risk of combo's at all, so if you actually make items available at those prices and let PC's buy more than one, you may be in for a ride. E.g. cloak, ring and ioun stone of protection are affordable by level 7, which is +3AC, +2 to saves. With armors+shield too, by level 10 you can get +7AC, +2 to saves - game math thoroughly broken now. And I bet there are more combos than just boring AC, too. \$\endgroup\$ Oct 25 '17 at 20:26
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    \$\begingroup\$ (Assuming the enworld.org/forum/… wealth-by-level's pan out). \$\endgroup\$ Oct 25 '17 at 20:26
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I don't know if the problem you are trying to solve is one of supplying prices for players trying to sell or buy magic items, or just finding a way to facilitate general magic item commerce. In the former case, the DMG has a very rough guide for prices based on rarity on page 133. If you are just looking for a way to allow players to buy and sell items, I would suggest using a modified barter system.

In my game, I decided that a believable (not realistic, that's another matter entirely) economy probably couldn't handle the huge sums that players want to transact on the spot. How much do 10,000 gold pieces weigh? How does Joe Shopkeeper store or transport that much gold without every thief in the city after him?

So I have instituted what I would call a magic broker, or agent. This is a person who can connect you with someone who might have the thing you are looking for, or at least something similar. He doesn't have an inventory of vorpal swords, but he knows a guy who has a dagger of poison he'd like to unload, and another guy with a +1 ax... He also knows an adventurer who really needs a potion of giant strength, and another looking for a ring of protection. In short, tell him what "magic surplus" you have, and he keeps a record. When someone comes along who needs it, he will contact you. For a small brokerage fee, of course.

He does have a small inventory of items that he knows will traffic easily (potions of healing, scrolls), but for the most part, he networks adventurers. It's a system that allows you to control the items available (no one can buy the arrow of dragon slaying that would derail your campaign, no matter how much gold they have), while allowing for interesting role play and barter encounters, back alley deals with dubious trading partners, and tough choices for players. All without creating Ye Olde Magic Shoppe.

Obviously, this choice works best in a large campaign city, with a high concentration of adventurers, but if your campaign has one nearby, it's a perfect spot.

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    \$\begingroup\$ FYI, 10,000 gold pieces weighs 200 lbs. Gems amounting to that value cold easily be transported by a person. Artworks and deeds to real estate can also have a very high value density. I like your general approach, and indeed upvoted your answer, but I don't think the limiting factor is really the existence and transportability of currency. \$\endgroup\$ Apr 28 '17 at 20:40
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Wizards have released an Unearthed Arcana article called Downtime that gives the players tasks they can pursue between adventures. These include buying, selling, and crafting magic items, along with prices based on rarity.

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    \$\begingroup\$ UA is play test material, but that is a useful tool for a DM if they feel the DMG does not suffice. \$\endgroup\$ Apr 28 '17 at 0:47
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Xanathar's Guide to Everything introduced a good way of selling and buying magic items, while information on the value of magic items can be found in the DMG.

The optional rules for Selling a Magic Item (XGtE 133-134) are part of Xanathar's Guide to Everything's Chapter 2: Downtime Revisited which is a two-step process of spreading the word and then determining the finalisation of the sale:

Resources. A character can find a buyer for one magic item by spending one workweek and [...] gp, which is used to spread word of the desired sale. A character must pick one item at a time to sell.

Resolution. A character who wants to sell an item must make a Charisma (Persuasion) check to determine what kind of offer comes in. The character can always opt not to sell, instead forfeiting the workweek of effort and trying again later. Use the Magic Item Base Prices and Magic Item Offer tables to determine the sale price.

The base price on the Magic Item Base Prices table (XGtE 133) is

Halved for a consumable item like a potion or scroll

and adjusted by the percentage rate in the Magic Item Offer table (XGtE 133) depending on the outcome of your roll during the Resolution phase.

During each workweek of the trying to sell a magical item Complications (XGtE 133) may arise, see the Magic Item Sale Complications table (XGtE 134).

Buying a Magic Item (XGtE 126) functions in a similar two-phase process of Resources (XGtE 126) and Resolution (XGtE 126) part of the Resolution phase is to make a check to use the Buying Magic Items table (XGtE 126) which dictates which Magic Item Table A-I (DMG 144-149) in the Dungeon Master’s Guide you use to determine which items are on the market.

The DM has the

final say in determining which items are for sale and their final price, no matter what the tables say.

The base price is displayed in the Magic Item Price table (XGtE 126), further Complications (XGtE 126, and corresponding Complications Table) may arise.

The Magic Item Rarity table (DMG 135) further defines the value of magic items corresponding to Rarity and Character Level columns.

When Buying and Selling (DMG 135) always consider that

Unless you decide your campaign works otherwise, most magic items are so rare that they aren't available for purchase.

When your campaign treats magic items as prevalent enough that adventurers can buy and sell them, then consult the optional rules and their corresponding tables, as detailed above.

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From UA_Downtime

Magic   Item    Price
Rarity Asking   Price
Common (1d6 + 1) ×  10  gp
Uncommon 1d6    ×   100 gp
Rare 2d10   ×   1,000   gp
Very    rare (1d4 + 1) ×    10,000  gp
Legendary 2d6 × 25,000  gp
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    \$\begingroup\$ -1 since this has already been mentioned in Paul's answer and doesn't add anything extra. \$\endgroup\$ Mar 9 '20 at 9:03

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