For simplicity we will ignore reserve requirements and such.
Consider a scenario where a customer had a $1mil deposit in the bank earning 4 %. This is a liability for the bank and they choose to use that money to purchase $1mil of bonds earning 5%. The government then spends that money through the economy ($1 mil deficit)and it ends up with another person who deposits the $1mil in the bank. The bank then buys another $1mil in bonds and the cycle continues.
So in this scenario there is not a debiting of anyone's account, the bank is just acting to balance it's liabilities and assets by purchasing bonds using the depositor's money.
For simplicity we will ignore reserve requirements and such.
Consider a scenario where a customer had a $1mil deposit in the bank earning 4 %. This is a liability for the bank and they choose to use that money to purchase $1mil of bonds earning 5%. The government then spends that money through the economy ($1 mil deficit)and it ends up with another person who deposits the $1mil in the bank. The bank then buys another $1mil in bonds and the cycle continues.
So in this scenario there is not a debiting of anyone's account, the bank is just acting to balance it's liabilities and assets by purchasing bonds using the depositor's money.
When the customer deposited the $1m with the bank, the bank was required to do appropriate double accounting. 1. It credited the customer's account with $1m which became a liability of the bank. 2. It credited an account of the bank with $1m which became an asset of the bank.
At that point in time the private sector had a money supply of $2m. Lending by the customer increased the money supply before the bank purchased bonds.
If the bank purchased $1m of bonds from the government it would debit its own account, and the government's account would be credited with $1m.
The private sector money supply has been reduced to $1m. The customer's money is unchanged but the bank's money has gone. The bank has replaced it's money with bonds (which are not money).
The government then spends $1m and returns that $1m to the private sector, restoring the private sector money supply to $2m - exactly what it was before the bond purchase.
The $1m initial deposit by the customer was never going to be retained by the bank and would always find it's way to being a deposit of another private entity ensuring the money supply would be still be $2m as a result of the $1m deposit in a bank.
That all make sense except the additional final step where the $1mil finds it's way into another depositor's account, thereby resulting in a total of $2mil in deposits. The bank then needs to invest the additional $1mil so that it's liabilities don't outweigh it's assets. It can choose to buy another $1mil of bonds if the government is continuing to run a deficit, thereby creating a further $1mil in someone else's account.
It's just the money multiplier effect at work and you could substitute the buying of bonds with loaning the $1mil to someone. As you say the money will then end up in someone else's account. The only limit to the process is the willingness of the bank to buy government bonds or alternatively, their ability to find a credit worthy borrower. The additional restraint is the bank's reserve requirements.
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