Why does central banks lowering interest rate incentivize more borrowing? I'm a layman trying to understand how the US monetary system works. I'm particularly interested in how the Federal Reserve can create inflation without printing new dollars and putting them in M1. My problem is that I don't get how the Federal Reserve can create inflation through lowering interest rates.
It's pretty intuitive on paper: when interest rates are lower people tend to demand more credit. Borrowing increases the M1 money supply. So we get inflation. I don't have trouble understanding that.
It's the other side of the trade that I don't understand. Why would a bank lend money at very low interest rates if that would create enough inflation that they'd be losing purchasing power? Maybe they do more than lending and it fits into a bigger picture that does make sense. But I can't find a good explanation of this.
Is there anyone that could explain/clarify this to me? I'm not an economist and the answers I find online are rather vague and complex for people like me in my opinion.
Thank you very much in advance,
Joshua
Banks lend because it is profitable for them to lend out money.  Banks do become less profitable in low interest environment, but they are still empirically able to maintain profitability, although there is evidence that goes hand in hand with some increase in risk taking (e.g. see Bikker &amp; Vervliet 2018). Consequently, the direct answer to your question is that banks expand their lending because it is still profitable for them to do so.
Additionally, if central banks would be really determined they could expand money supply by open market operations (e.g. purchase of government bonds) and various other channels, so if a determined central bank would want to expand money supply it can do that whatever the private banks are doing.
Furthermore, inflation does not necessary means that the bank will become worse off. If there is 2% inflation in an economy but bank's profits increase by 5% during the same period then a bank is still better off in real terms.
Lastly, there is not necessarily 1:1 correspondence between increase in money supply and inflation.  For example, even in a simple money market equilibrium model (which determines price level - increase of which is inflation) given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY$$
Where $M$ is the money supply, $V$ velocity of money, $P$ price level and $Y$ output.
Solving for price level and log-linearizing we get:
$$\ln P = \ln M + \ln V - \ln Y $$
Consequently, ceteris paribus, if $M$ increases by $1\%$ and $Y$ increases also by $1\%$ then the net effect on price level will be zero (and consequently inflation will also be zero). Even in this simple model you will only get inflation if $ \ln M + \ln V - \ln Y &gt; 0$ so when bank increase money supply it won't necessarily result in an equivalent inflation. Furthermore, in more complex models inflation depends on other factors such as people expectations meaning the relationship is not necessarily even proportional, but discussing this in depth would be beyond scope of this answer.