I'm a syndicated writer working on an explainer about income inequality and I realized I didn't really understand how it can possibly develop in an economy where all dollars are spent. That is, let's take a hypothetical: I understand how it's possible where one person creates a product that everyone else purchases (creating a concentration of wealth). But, then, that person invests or saves the money, which ultimately gets circulated back into the economy. If total money is zero-sum (all saved money is spent, all received money is spent), how does any one actor in the system end up with more money than others?
As I see it, the only mechanisms by which income inequality could increase within a group of people is if the system included globalization, where wealthy people spend money outside of the system (i.e. sending the money to other countries which were previously poor)
I'm open to answers that include a closed hypothetical economy (with 3 actors) or some other explanation. Thank you and let me know if I can clarify this question.
Update: Some have suggested its a duplicate of "how wealth is created". This is different because im asking about income (money supply and distribution), not the distribution of outputs. I get how some people might produce more. I dont understand how money concentrates in a system where all savings is invested or spent.