Why have things gotten so expensive even though the central bank has a mandate for full employment at low inflation.

It has to do with the base effect.

Central banks, as a practical matter, have chosen an inflation rate of 2% as their target for low inflation. The idea is that that is hopefully far enough away from deflation to prevent across the board deflation, which is very destructive to an economy, and at the same time is hopefully low enough that people won't notice it too quickly.

The problem is that even at 2% inflation, many things will eventually get very expensive.

This is because even if everything is just going up in price at 2% a year, items that were more expensive to begin with will be going up in price at a higher rate in absolute terms than items that were less expensive to begin with.

But most people do not have really high incomes. So although they will be getting raises along the way, those raises will not be high enough in absolute terms to keep up with the rate at which the more expensive items are going up in price in absolute terms.

So if enough time goes by, most people will be priced out of the more expensive items. I think we have at least just about reached that point.

And if even more time goes by, or there is a higher inflation along the way, like we had recently, then a lot of people will ultimately even be priced out of a lot of less expensive items. I think we have also at least just about reached that point.

The overall point I am trying to make here is that if the authorities try to keep things going forever, the situation is eventually going to reach a point where things are effectively totally out of reach, totally out of whack. Because that is simply how the math works. (Noting that I am talking here about a sophisticated economy, not a primitive one.)

And so if things go on for long enough, most people will be left in the lurch.

That is simply the reality of the situation. There is no way around that. The math is inescapable.