Eliezer_Yudkowsky comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong Discussion
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Trade is a bigger problem than theft.
It's (relatively) easy to handwave into being prohibitions on theft -- pretty much every society dislikes it and you can posit both morality and anti-theft magics as making outright thieving to be not too useful for wizards.
On the other hand trade is generally seen as good and there are huge and obvious benefits to trade between Muggles and wizards. Especially given how easy it would be for less scrupulous wizards to make sure the terms of trade are very very beneficial to them (and yet do not descend into outright theft).
I'm not sure the problem is solvable without introducing major new mechanisms of how the world works.
Many, many post-agricultural societies have restrained trade, often to particular privileged individuals. I believe this is what a 'patent' used to be.
Yes, but notice what this implies. This implies that trade is such an awesome value-producing mechanism that we (=elites with political power) want to keep it for ourselves and our friends.
The idea is not to forbid trade, the idea is to restrict access and thus collect what the econospeak calls rents. Everyone wants to be a gatekeeper at a fountain of gold.
This usually requires that the person holding the patent provide enough trade to satisfy demand. Otherwise the pressure to create a black market is irresistible. So trade could be restricted to a few powerful wizards - perhaps to each wizarding government - but it could not be eliminated entirely.
And since wizards can provide extremely valuable services to Muggles in trade, they would capture almost all the Muggle gold in return. Then we would observe wizarding billionaires, making fortunes of a 100,000 Galleons negligible in comparison. That we don't observe this is strong evidence that trade either doesn't exist at all or is universal and unrestricted. Since the story offers ample proof that trade isn't universal, it must be nonexistent. But it's not clear what is preventing trade.
Wizarding culture. Trade with muggles was basically worthless until a single wizard's lifetime ago, so the prejudice hasn't had time to evolve away yet.
Muggles had a lot of gold a hundred years ago, too. Certainly if you count in terms of just a few wizards taking possession of it. And it was easier to find because currencies were gold-backed.
If they were unwilling to just steal it (for whatever reason), then spending a few weeks performing services for the richest people in the world in exchange for half their wealth (amounting to many millions of Galleons) would have been a great bargain for wizards.
I recall reading that somewhere (maybe Pottermore?), Rowling said that the Malfoys gained their great family wealth by trade with muggles, until the establishment of the statute of secrecy, at which point they were quick to join the "Yep, we knew those dirty muggles just wanted to exploit and burn us all along!" crowd. I don't remember if there is any similar detail about other wealthy families in canon or MoR; there's Flamel with the Philosopher's Stone, and the Potters with a combination family inheritance/bounty on Voldemort, but the Malfoys appear to be decidedly the richest family in Magical Britain, and I'd imagine that even with a 400 year gap, being those to most thoroughly exploit trade with muggles would be more than sufficient to explain their success.