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"As such, some of the deposits would have to be interest-bearing in order to generate a sensible asset mix for the household sector and the non-bank business sector."

They become interest bearing by the action of competition. Banks will pay nothing on deposits by default. However that gives some banks an alternative commercial strategy to insert themselves in the chain by being a 'wholesale depositor'. They can attract away deposits by paying interest, then bank the transferred reserves at the central bank and get paid the deposit rate the central bank is offering (assuming rates are above zero), or buy government bonds. This is nothing more than 'lending to government' (notionally of course) rather than 'lending to the private sector'.

Unless 'lending to the private sector' banks respond by increasing deposit rates, then they would be forced to the discount window.

The end result is banks becoming part wholesale depositor and part lending bank with a mark up on top of the market clearing rate for deposits, at least until some idiot introduces tiered interest rates, or reserve requirements...

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