The annual student intake of Hogwarts seems about 100. Since in book 7 Hogwarts is declared mandatory for all children, this means that the total magical population of Britain cannot be much more than 10,000.
How do these people make a living?
All jobs mentioned in the books are non-productive occupations (government, stores, sports &c) - not farmers or engineers. There are exceptions - makers of wands/robes/broomsticks - but where do they get the raw materials from?
Who and how "creates goods" in the wizarding world?
Note that if you say "wizards exchange their gold for Muggle money and buy stuff from Muggles (through intermediaries, if necessary)" then you would have to explain where they get their gold: they would either have to mine it, or produce something of value to the Muggles (in which case the separate financial system of galleons/sickles/knuts does not make sense).
PS. A simple issue of maintaining a steam locomotive for Hogwarts express is pretty much insurmountable for 10k people - without Magic, that is. So, I can imagine that the skilled tradesmen can transfigure dirt into raw materials for their trade - except for food, which "is the first of the five Principal Exceptions to Gamp's Law of Elemental Transfiguration".
Answer
TL;DR:
To misquote an apocryphal Tolkien-derived work "The last Ring-Bearer": "It is rather hard to analyze the reign of the first Princes of Ithilien, Faramir and Éowyn, in political or economical terms – it appears that they had neither politics nor economics over there, but only a never-ending romantic ballad".
In other words, Potterverse has no economic system we can coherently and logically deduce or find, because Rowling didn't put one in.
In-universe details:
You have to remember that Potterverse's Wizarding world is a weird combination of magic (meaning, a lot of their basic needs are taken care of "for free", except for food - basically, they are closer to Star Trek's Post-scarcity economy than to anything else), and late medieval/early modern Muggle society, which is when they separated from Muggles - culminating in full separation under statutes of secrecy in 1689.
As such, there seems to be a somewhat late feudal/early bourgeois trade system (you have trade shops, such as Madame Malkin's clothing, or Ollivander's Wands, or Zonko's, or various inns/taverns). You have a primitive bank (Goblin) that doesn't appear to do anything aside from holding money and valuables and facilitating ForEx trade (e.g. muggle money exchange). You have a very large government that pays salaries and seems to employ a large proportion of wizarding population.
There doesn't appear to be anything like a capitalist system (rich families are rich because they inherit old money, except for a rare and likely unique case of a startup in the form of Weasley's Wizarding Wheezes with Harry as angel investor). There's no mention of investments aside from that, or from capital accumulation, etc...
However, we ALSO don't see a proper feudal system, with no vassals being granted land by their liege lords.
As a matter of fact, aside from Weasley's garden and Hagrid growing some produce in Hogwarts, we don't see ANY agriculture... despite food being the one known exception from being magically created out of thin air.
Out of universe, this is explained by 2 things:
These are magic books for child audiences. What do 11-year-olds care about economics? Most boring subject possible.
JKR isn't exactly an economics maven. She went from a welfare case to multimillionaire practicably overnight, and as far as I'm aware was a liberal arts major/worker before that, and based on some of her non-Potter writings, has a very poor understanding of what makes economy tick.
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