Private bank lending on a fiat standard is always increasing the money supply.

Fiscal deficits increase the money supply if the debt is monetized by the central bank.

The US is already running a large deficit with a high debt to gdp ratio. This will lead to a debt spiral and no other option than monetizing the debt. QE infinity …

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However, Biden is talking of price inflation (not monetary inflation) which government spending definitely increases.

There's no such thing as "price inflation". It's a term coined by fiat institutions to distract people and to evade straight consequensies of excess money printing.

There's many things on the market that affects prices but inflation/deflation are definitely the main drivers.

I agree that it is a term coined by fiat rent seekers to distract people from the real monetary inflation. However, that doesn’t change the fact that price inflation (or call it price changes) exists.

And it doesn’t change the fact, that Biden is talking about price inflation. For that reason your response arguing about monetary inflation is therefore missing the point.

However, well done on grasping the principles of Austrian economics.

I have read Mises, Hayek, and Rothbard, so there's no need to instruct me on Austrian economics. Nevertheless, I appreciate your efforts.

Does private bank lending bitcoin always increasing the money supply?

I am talking about a fiat standard and you come up with this question? As if private banks lend you bitcoin …