In a discussion of income inequality, the most relevant factor is excess capital. For those on the bottom of the ladder, whose money goes toward basic expenses, this potentially virtuous cycle is completely out of reach. Their money is best spent on purchasing stability rather than attempting to secure wealth. For those in the middle nurturing already-comfortable lives, the upside of shooting the moon in an attempt to gain wealth is often outweighed by the risk of sustaining financially disruptive losses, as well as the discomfort inherent in turning away from a lifestyle that pleases them. [1]
Then there are the wealthy. I'm not talking about the faux-wealthy whose lifestyle preferences drive them to buy Maseratis and condos on credit and spending the rest of their lives wearing golden handcuffs. I'm talking about those who have money left over after they've secured themselves a comfortable lifestyle. They have excess capital. Ten thousand dollars can go into the stock market, a hundred thousand dollars can go into a small business, a million dollars can go into a more sizable business, ten million can go into multiple sizable businesses, etc.
The opportunities for growth scale with the size of your disposable income. If you take this view, it suddenly becomes stupidly obvious why the one percent of the one percent makes so much more than the ninety-nine percent of the one percent: they had more to begin with. I'm all but certain if you zoom in on the the one percent of the one percent of the one percent, you'll see a similar disparity.
Unrelated corollary: This also helps to explain both why traditional entrepreneurs are older, and why tech entrepreneurs tend to be younger: non-tech leaders spend their lives amassing wealth, techies are so in demand they get a good dose of it when they're young. Although the acquisition appetites of behemoths like Google and Facebook certainly don't hurt.
[1] I'm so certain someone will respond to this comment by quoting that one study where happiness flattens around like $75,000 that I won't even bother finding it myself.