Doesn't sound right. Muggle born wizards had to probably find a way to exchange muggle money for wizarding money. 

So not only is the wizarding economy almost completely decoupled from the Muggle economy, no one here has ever heard of arbitrage

Hits very hard and resonates strongly with many relationships in life!

And I know that I'd just make myself unhappy by comparing that reality to... something perfect that I built up in my imagination.