I just read parts of an introductory economics book. I read about the monetary system in the U.S. and came up with the following question:
Can the Fed raise the M1 money supply permanently without having either to buy further Treasury bills or use helicopter money (i.e. to refrain from recieving the principal payment at maturity) ?
I think about the following model:
There is the Fed $F$ the companies $C$ the households $H$ and the banks $B$. We can partition the system into $\{F\}$ and $\{B,C,H\}$. At time $t=0$ there are $\alpha$ $\$$ in $\{B,C,H\}$ as currency i.e. as physical bank notes. No matter what happens in $\{B,C,H\}$ $\alpha$ cannot increase. Suppose $F$ wants to increase the money supply. As far as I know the Fed primarily uses open market operations (OMOs) to increase money supply. Let's try this. To simplify things let's consider a very simple bond. Someone in $\{B,C,H\}$ issues a bond for $\beta \$ $. The terms of the bond will grant the buyer a payment of $\gamma \$ $ at $t=1$ and $ \delta = \gamma - \beta > 0$.
So, as the Fed wants to increase money supply it undergoes an OMO, i.e. prints $\beta \$ $ and buys our bond. The money supply in $\{B,C,H\}$ at $ 0 < t <1 $ is $ \alpha + \beta $. So far so good. We could consider the money multiplication buy loans during $ 0 < t <1 $ but that would not change the situation at $ t > 1$. At $t=1$ the issuer of the bond i.e. someone in $ \{B,C,H\}$ has to pay $F$ $\gamma \$$. So, at $t > 1 $ there is less money ( $ \alpha - \delta$ ) in $\{B,C,H\}$.
So, to me all of that seems controversial. $F$ wants to increase the money in $\{B,C,H\}$ but effectively reduces it. Of course $F$ could disguise the situation by buying another bonds and thus increase the time until maturity but this does not really change the situation. So, this question comes up:
Can the Fed raise the M1 money supply permanently without having either to buy further Treasury bills or use helicopter money (i.e. to refrain from recieving the principal payment at maturity) ?