Although a sadist is one way to describe him, The Joker is much more large scale than that. His psyche was accurately described by Alfred J. Pennyworth in "The Dark Knight" when he said "Some men just wanna watch the world burn". The Joker is definitely a sociopath since he is as indifferent to morality as can be.
The Joker, as depicted in Christopher Nolan's film, is an anarchist. His goal is to bring about chaos in the world. By burning the money, he is demonstrating that he does not care about money; he just, in Alfred's words, "wants to see the world burn."
At no point was the Joker actually "paid" for his services. He merely burns all of the money as a display of his wanton disregard for the value of currency.
What does Joker say when he burns the money?
JOKER: Oh, I am. I'm only burning my half. (Lights the money pile) All you care about is money. This town, it deserves a better class of criminal, and I'm going to give it to them.
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Short StoryThe Joker is a supervillain who appears in American comic books published by DC Comics. The Joker was created by Bill Finger, Bob Kane, and Jerry Robinson and first appeared in the debut issue of the comic book Batman on April 25, 1940. Credit for t...