"No spell can reawaken the dead."
     -- Albus Dumbledore

Magical Theory:
The Limits of Magic
by Caius Marcius

We all know the amazing things that magic is capable of in JKR's narrative. I'd like to look at some of the things that magic is apparently unable to do in the JKR universe (as opposed to things that Wizards don't do, such as the Unforgivable Curses, for legal reasons or because of societal norms):

(1) Magic can forestall death, but it cannot resurrect the dead. Wizards are able to extend the normal human lifespan; the Elixir of Life, a byproduct of the Philosopher's Stone [that's the Sorcerer's Stone to us Americans. -ed.], can make its drinker "immortal". However, the Elixir is exceedingly rare and difficult to obtain; its only known users, Nicholas and Perenelle Flemel, measure their lifespan "only" in terms of centuries, not millennium; and when the Philosopher's Stone is destroyed, the Flamels surrender to their mortality.

(2) As we all know from our frequent visits to Madame Pomfrey's infirmary, magic can treat a variety of ailments and injuries in a manner far beyond our medical technology.  Perhaps her most amazing intervention was to regenerate the bones of Harry's arm after Lockhart inadvertently made them vanish. But there are limits on what medical magic can effect. The case of Mad-Eye Moody is perhaps the best example: he is hideously scarred from his many battles with Dark Wizards, and has lost (though the details of his encounters remain frustratingly vague) a leg, an eye, and part of his nose. For some reason, his injuries could not be repaired. This may be due to the design of the Dark Wizards' hexes, which we may assume are intended to be irreversible. To be fair, this may also be by choice: Moody very likely enjoys the fear his ghastly appearance generates. But Neville Longbottom's father, who was also an Auror like Moody, and his mother were driven incurably insane after being
tortured by  Dark Wizards in search of Voldemort's whereabouts; they are now hospitalized at St. Mungo's Hospital for Magical Maladies and Injuries, and do not recognize Neville when he visits. And of course, Harry himself wears glasses and no one has offered to fix his vision with magic, something they would certainly have done for him if it were possible.  There are clearly limits, then, on what magical medicine can do.

(3) Skills and knowledge cannot be obtained by magical  methods. There is no spell than professors can perform upon their students to fill their noggins with the requisite magical knowledge: still less can students perform such spells upon themselves when finals are approaching (or George and Fred would have surely already done so). We've heard little about cheating on exams at Hogwarts, save for anti-cheating charms that the professors make use of, but I would suppose that a would-be cheater would be compelled to resort to pretty much the same methods that his Muggle counterparts might employ. Otherwise, the honest Hogwarts student must laboriously assimilate knowledge the same way we mere Muggles acquired our degrees: through intensive study, rote memorization and practice, practice, practice. Hermione, the scholar par excellence, stands out  in the same way that she would  stand out had she remained in the Muggle world – through her diligent and painstaking study, or as one law school student once described it, the chronic and habitual application of butt upon chair. 

(4) Most poignantly of all, material possessions cannot be magically acquired, and stigma of poverty cannot be covered up through magical means. Harry can summon his Firebolt when he battles the Hungarian Horntail, but he can't transfigure a rock into a flying broom (as Cedric transfigured a rock into a dog). And this isn't merely due to his youth and inexperience: Sirius Black, a skilled and experienced Wizard, must purchase the Firebolt for Harry much as we might purchase our gifts off the Toys-R-Us or the Lands Ends website. 
Similarly, Remus Lupin knows how to deal with Boggarts and Grindylows,  but he can't conceal his shabby looking robes "that had been darned in several places," or his battered luggage which must be held together with string rather than magic. Arthur Weasley can erase the memory of Muggles and can charm a car to fly, but he can't make the Burrow look like anything more than the cozy but dilapidated hovel that it is, or provide a new wardrobe for his children. Ron must wear hand-me-downs and clothing too small for him, and complain of his poverty. The wealthy families, such as the Malfoys, have seemingly acquired their pelf in much the same manner as Muggles families.

The restrictions on economics may reflect the fact that the Wizards live in a capitalistic society. A great portion of the Wizarding world's populace make their living through commerce, and it would be destructive of their livelihood if other wizards could magically create the good that they offer. Why go to Diagon Alley if you could magically create your own robes,  wands,  textbooks, and Bertie Bott's Every Flavor Beans?  Now, perhaps the laws should be altered so that every wizard could magically create what they needed? But a society where every person is totally self-sufficient would be ungovernable, just as a person who could satisfy his every desire would become quickly bored and satiated.  As Dumbledore tells Harry at the end of SS/PS, "As much money and life as you could want! The two things most humans would chose above all – the trouble is, humans do have a knack of choosing precisely those things that are worst for them."

copyright 2000 by Caius Macius