An argument against inflationary monetary policy

(I’m using “inflation” in the Austrian sense here: increase in the money supply, rather than increase in CPI price levels)

I just heard this recently, and it made sense to me:

1. The entire Keynesian scheme of monetary/fiscal spending to stimulate the economy only works because it takes time for people to catch on to the reality that newly printed paper is not real wealth. That is, people don’t immediately realize that they are spending fiat-money, and thus act based on thinking they have more money than they really do.
2. This temporarily causes greater investment, which has the potential to create real wealth and real economic growth.
3. However, as time goes on, sellers realize that buyers have more money, and thus prices rise accordingly, bringing the economy back to status quo ante, except with possibly increased debt (if enough real economic growth did not occur before the sellers caught on).
4. In the case of monetary policy specifically, newly printed money inevitably goes to the rich first: to banks, and from there to massive corporate investments.
5. As time goes on, more of the poor get the new cash, but it also simultaneously becomes less valuable, since prices are rising.

Thus, monetary policy seems to be, inevitably, welfare for the rich.

(Note that none of this would be an argument against government welfare, based on tax-hikes (not spending fiat money), for the poor.)