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I have always thought that groups of individuals that spend more money(as opposed to save) have more money in the long run. My reasoning is that if a particular group spends money, then each dollar that one person spends is being used by more individuals, and thus one physical dollar, might have a value of $10/day. (spent 10 times a day)

While if a group does not spend money, then one physical dollar may only have a value of $0.1/day. (spent once in ten days)

Is there any logic in my thought process?

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This idea is studied in economics, where it is called the velocity of money.

You should be careful that not all transactions create value in the same way. If you pay me $\$1$ to erase your blackboard, this is equivalent to and creates the same value as if you sell me the dirty blackboard for $\$100$ and then buy it back for $\$101$ once it is clean. However, the total size of the transactions may look different, $\$1$ versus $\$201$.

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