The problems start when the rich get richer faster than what it takes for the poor to get a little less poor. This is what is described as 'divergent behavior'.

The problems start when the rich get richer faster than what it takes for the poor to get a little less poor. This is what is described as 'divergent behavior'. In the long term there is no equilibrium to this, and we revert to pre WWI Europe levels of inequality. What happens then to reduce inequality is anyone's guess, but in the XX century the Russian Revolution, World Wars, and the Great Depression have been very effective. Other than that one could make the point that for someone who is already very rich, getting marginally richer doesn't do much while lifting someone from abject poverty is something that has a great effect on that person's life (in other words utility is probably sub-logarithmic).