I didn’t notice this at first, but one of my friends pointed out that most of the wizarding labour in the Harry Potter universe seemed to be employed by one of two employers. As a graduate of Hogwarts, you could respectably become a teacher at Hogwarts, or a civil servant of some description in the Ministry of Magic. Or you could leave the wizarding world and live a low-key existence amongst the Muggles. Appointments to either Hogwarts or the Ministry of Magic are conditional on you performing exceptionally well in a number of exams.
It then hit me that the Harry Potter world is actually an implementation of Confucius’ vision of society, complete with all the flaws in such a system!
The bureaucracy of the Ministry of Magic is sprawling and has an almost totalitarian (but not necessarily adversarial) influence over wizarding life. The same people constitute the executive, legislative and judiciary branches, with no separation of powers. There is only a very small private sector, and the state does not practise outsourcing.
Entry into the wizarding world is in theory open to all that display magical abilities, but in practice such abilities run mostly down bloodlines and there are relatively few Muggle-borns. While Muggle-borns are no less talented than their pure-blood colleagues, they nonetheless face either explicit hostility, or subtle prejudice. Such prejudice is common within the pure-blood aristocracy, with dissenting voices being rare and limited to liberals such as the Weasley House, who have some, but not much, political influence.
The Ministry of Magic is mostly concerned with policing the activities of wizards, and is uninterested in the Muggle world, for the most part desiring neither to improve nor oppress the latter. Like the Party in Nineteen Eighty-Four, the Ministry is concerned with staying in power and focuses its efforts on fighting potential rivals such as Albus Dumbledore, rather than effectively addressing the evils of society.