I've been curious what stops wizards from creating and endless supply of wizard currency. After looking at a few other questions (like this, and this) it keeps getting stated that wizards can't create the precious metals needed to create more of the wizard currency. However it doesn't appear to be explained why they can't create those precious metals. I was hoping someone could explain why, what about magic limits it's use so it can't be used to create precious metals?
In addition to Slytherincess' excellent answer, you have to remember that in UK wizarding world, the bank(s) and currency is controlled by goblins. This leads me to believe that goblins are also responsible for the creation of currency.
Now yes, theoretically, someone could make another Philosopher's Stone, which they then use to turn some basic metal into gold, then magically melt it down and shape/design it to appear as a real Galleon. However, goblins (who again control and likely forge the currency) are able to distinguish the subtle differences between goblin made metal items and wizard made replicas of said items (i.e. the Sword of Gryffindor in the Deathly Hollows). This would hold true for any wizarding counterfeit currencies.
Now think of this from a governmental perspective (a little off topic, but there it is). I don't know about other countries, but in the US, there is, and always has been a problem with dishonest people attempting (and in many cases succeeding) in counterfeiting currency. By allowing goblins, the one race that can forge metals in ways humans (wizards included) are unable to, and can distinguish the difference between goblin made currency and wizard made currency, you effectively control how much counterfeiting can be done, as the counterfeit currency would never make it past the bank!
Is this likely to prevent someone like Mundungus from creating a counterfeit galleon and passing it off at a shop in Diagon Ally? Probably not, but I am sure the wizarding world is probably advanced enough to be able to trace a counterfeit (once identified at Gringotts) back to the creator.
Well, wizard Nicholas Flamel, owner of the Philosopher's Stone, could have had the capability to make gold using the stone, gold being a precious metal.
As far as I'm aware, nowhere in canon does it say that wizards cannot make precious metals (And the existence of the Philosopher's Stone in the Harry Potter universe would suggest otherwise.). Actually, nowhere, I believe, does it say that money cannot be made magically -- meaning, it doesn't state this outright. However, my canon-based guess is that the creation of precious metals for the sole purpose of creating currency would perhaps violate Gamp's Five Laws of Elemental Transfiguration.
I think it's important to remember that metals considered precious by humans may not be considered as valuable by wizards -- perhaps metals other than gold, silver, or bronze might have more magical properties, and therefore be more valuable in the wizarding world. Just an idea.
I think of Magic as not being able to "create" but it can "summon" or "transform." For instance, any magically-produced food is either transported from a remote kitchen, or derived from available energy + matter. In the case of gold, since no one knows the "recipe," the only way to conjure up real gold is to transport it from another location. If you owned it, then it is legit. If not, they you just stole it.