“Purely mathematical approaches to the economy have a big drawback: the irrational behaviour of people.”

This seems like nonsense. Are people more chaotic than the weather?

Most things are chaotic, and provably unpredictable at the micro level, but that does not make them unstudyable, in terms of mathematics. Secondly, people are clearly not totally irrational, so one might expect the rational behavior of people to be the unusual feature in an otherwise totally chaotic system.

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