Money serves as a unit of account, a medium of exchange, and a store of value. That's textbook.
Money enables us to set a price on things, and to reduce the friction involved in buying and selling them. You want to sell your barley to buy my coal? You sell your barley for money, give me money for coal, and we're both happy. Without money, you'd have to barter, and if I don't want your barley, you'd have to figure out what I do want, find somebody who has that and is willing to swap for barley, and then bring that to me and complete the exchange. Without money, buying and selling is a big pain. People would make fewer things and less of them, because they'd be hard to sell, and they'd sell within their own village, except for a few wandering trading speculators. It's the kind of economy you get in a serf society.
I think there's a fourth fundamental purpose to money, which is: money liberates peoples' ability to specialize and create objects and services of value. Human beings simply can't, or won't, create wealth without an effortless means of transacting exchange. Humans are different creatures because of money; they are more human than they would be without it.
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