Is Inequality in America Irreversible?

I recently read a very interesting book by an American academic and activist Chuck Collins - 'Is Inequality in America Irreversible?' which discussed the obscene level of poverty in the US. We don't often hear about the row upon row of people in downtown LA who are sleeping on the streets amid faeces, rats and rubbish do we?  He gave an interesting list of changes which need to be made and legislation which needs to be introduced to reduce inequality.
It seems to me that the big question is 'How can we persuade the mega rich - what I've come to see as the wealthy 'Mafia' - to give up some of their goodies so that those living in abject poverty can have a fair slice of the cake, a semblance of a reasonable life?'
Our planet is finite.  As Gandi said, the planet can provide for everyone's NEED but not for their GREED.  So, it makes sense to me that to bring about some degree of equality, the rich will have to  give up the luxury yacht, the expensive fashions and the two or three homes dotted around the world. Can we realistically expect that to happen?  I suspect not.
Interestingly, my reading of Chuck Collins' book coincided with a report being published in the UK which says that the government's introduction of Academy schools has increased inequality in the UK by giving children from a poor background a reduced opportunity for a good education.  So much for reducing inequality ...
If we are really serious about reducing inequality we must work out how to challenge the power of the mega rich