If the rich getting richer drives up inflation then that does indeed mean that the poor get poorer.
Big if! (Inflation drives both price levels and wages.)
Also even if wages go up inflation still reduces the wealth owned by the middle class. Especially given that interest rates on savings hasn't kept pace with inflation for decades. So unless you own a house or a stock portfolio even the middle class gets poorer due to inflation.
Yes. That’s a pretty critical question.
High inflation drives inequality. (Moderate depends on the savings rate.) We have zero evidence inequality drives inflation.
That is not how the saying goes.
https://en.m.wikipedia.org/wiki/The_rich_get_richer_and_the_...
It’s said as a statement on policies that benefit the rich and hurt the poor, not on fixed money supply.