Explaining the development of income inequality 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.
First off, dollars are not the sole determination of wealth.  People can be wealthy by having a large house and a nice car and still have \$0 in the bank.  Dollars hold wealth only because they can be exchanged for goods or services that actually do have value.  

With that being said, let us take a look at what you have asked: 


  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? 


The two phrases that I have emphasized above, hold the answer to your question.  In fact, you have almost answered your question in the first phrase.  

The only reason that wealth has concentrated in Person A (who creates a product that everyone else purchases) is because everyone else has determined that they would rather have that product than the money that they have.  The benefits of having that product outweigh the benefits of keeping the money.  Many economists would argue that everyone is better off because the seller has improved his life by getting more money and the buyers have improved their lives by getting the better product.  

Now, what does Person A do with the money?  Person A does the exact same thing that everyone else did originally: he looks for products that he would rather have than money.
In the marketplace, Person B, Person C, and Person D are all selling unique products of their own.  Person A sees value in purchasing the products from Person B and Person D, but values his money more than the product from Person C.  So, Person A purchases from Persons B and D but not from Person C.  This means that the money flows from Person A to Person B and Person D.  

This cycle will continue to repeat indefinitely.
As long as Persons A, B, and D continue to produce products that people value more than money, they will continue to gain wealth.
On the flip side, as long as Person C does not produce a product that people value more than money, he will not gain wealth.