You just described the problem with inflation perfectly.
Prices go up - whether it be money supply created or supply side created. The wealthy benefit from it first - whether it be access to ZIRP funds you don't have access to, or they get to recoup increased goods sell prices before the workers get a raise. Hence the issue with inflation - it naturally benefits the ultra rich first and foremost.
Look no further than the UAW. They are all proud of there negotiated wage increase - except GM has 3 years of record profits already under their belt so they never catch up. In there case there still luckier than the average worker, because they will keep those raises, the rest of us just get laid off.
So the decline of the middle class continues.