So it is inflationary according to your definition
So now you’re talking about not being a rise in prices.
Under a free banking system, unless the recipient of MOTS’s check is a client at the same bank as Mr. MOTS, the recipient of the check will deposit the check in his own bank. When his bank attempts to redeem the check, the bank of Mr. MOTS is found to be insolvent.
Under central banking, the central bank will coordinate this process by essentially acting as a clearance house. It will make sure that all banks expand at the same rate so that the above doesn’t occur. If Mr MOTS’ bank also receives a deposit by one of its clients with a check belonging to the same bank that had received the check from Mr. MOTS’ recipient, then the two can cancel out their debts to one another by simple book keeping
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The fed lending banks money is just one of the tools available to facilitate the above coordination process. The major point that you have missed is the multiplier factor that results from the process of credit expansion. At the end of the expansion, the bank will have pyramided approximately $900 on top of the original deposit of $100. So the money supply has increased from $100 to $1000. That’s where most of your inflation comes from.