There are two basic ways to make money in a capitalist economy. One way is through labor -- you can trade your time for money. The other is through investment -- you can trade your money for more money. There are plenty of ways to do this -- stocks, finance, hedge funds, but they all share the feature that, if you start with twice as much money, without any more work or skill you make twice as much money.
Each round of the simulation, everyone spends money, then the money is divided between labor (think employees) and capital (owners/shareholders, lenders) with wages and return rates varying randomly. Money not spent is invested so that returns to capital are distributed in proportion to wealth. For spending, a certain amount is considered "necessity," by which I merely mean the minimum amount of spending that will be done by someone who isn't living paycheck-to-paycheck. Luxury spending rises in proportion to wealth.
What can you learn from a model obviously far simpler than reality? One is that the mere fact that money can be used to make more money is sufficient to explain the sort of extreme concentration of wealth seen in our economy. Conservatives often suggest differing degrees of talent or education as a reason for inequality; protesters in the Occupy Wall Street movement note that the rich use money to buy influence to further rig the system in their favor. (And both claims may have some merit though neither is incorporated in my model.) In both cases they are trying to make a moral case for or against inequality by arguing whether the wealth of the superrich is deserved. I have more practical concerns. I want to know whether a capitalist society that neither does anything to create inequality nor prevent its growth to extreme levels is sustainable over the long term.
The main question I wanted to answer with this model is: is inequality self-stabilizing? That is, should we expect that, given no major changes in the economy, the super-rich will get a little richer but then stop seeing their share of the wealth grow, or is it more likely that wealth will continue to be concentrated in fewer hands if nothing fundamentally changes? The latter case is familiar to anyone who's played Monopoly; the rich keep getting richer until there is no money left in anyone else's pocket.
What I've found is that just about any balance between capital and labor that give the top 1% 35% of the wealth will eventually give them 90% of the wealth or more. So am I missing any important stabilizing processes?
For decades following World War 2, tax rates on the wealthiest were kept at 90%, making it quite difficult for the rich to get richer. As this tax rate dropped, inequality took off and it has shown no signs of stopping. As globalization and automation shift the balance of power further toward capital at labor's expense, it's hard to see what would stop the continuing growth of inequality unless we decide once again that we will deliberately stop it.