And another point:
One of the major ironies in economics is Keynesians' use of the fallacy of composition to explain why, allegedly, saving might be good for the individual but not for the group. But, in fact, the greatest commission of the fallacy of composition is committed by the Keynesians themselves. They build an entire corpus of economics on each business-person's understanding that if demand for his firm's output rises, his firm (and his workers and other suppliers) are made better off. Keynesians reach exactly the same conclusion that most business people reach, namely, if higher demand of my output is good for me, then higher demand for everyone's output will be good for everyone — for the entire economy.
That is a perfect example of the fallacy of composition.