Central Banking: The Process of Bank Credit Expansion
Expansion from Bank to Bank
So far, examples have not considered transactions in isolation, and have not followed them further. With competitive banking (multiple independent banks), funds flow from bank to bank, and the problem is compounded.
On $1000 in reserves, Bank A makes $4000 in loans. When those funds are deposited in bank B, it can then use the deposit ($4000) as a reserve to float $16,000 in loans. When those funds are deposited in bank C (or even back into bank A), it can then use those funds as a reserve to float $64,000 in loans. By this process, money grows exponentially: the ultimate amount is still backed by the original reserves ($64,000 backed by $1000).
As the loans are repaid and cash flows back through the chain, the "new" money in circulation likewise decreases back to its original $1,000 - however, at any given time, the amount of debt in an economy has a corresponding impact on the inflation in that same economy.
The Central Bank and the Treasury
Some mathematical examples to demonstrate that the surplus or deficit in a government treasury has no necessary impact on the central bank, nor vice-versa, except in extreme circumstances (such as a government's collapse).
The fact that the government treasury issues and buys back bonds simply makes it another customer of the central bank. By modifying the reserve rate and buying./selling debt to commercial banks, the central bank can mediate any effect that government spending might have on the national economy ... with the exception of inflationary impact.