Why can John Cochrane close the loops and span the banking tree and find the equilibrium points? Because he, unconsciously (or consciously) knows that the currency function is simply the master spread sheet that maintains a unit of price variance, suitable as a numerator in price.
All the rest of banking still exists, its all important, dealing with government is always a mess. But at its core, the unit of account is simply a shaped probability distribution. It is a distribution of deposits and withdrawals of member banks, and when that distribution reaches some threshold, the spreadsheet resets the clearing function. The clearing function always pushing the probability distribution, optimally, back into shape.
It can be no other way, it is the definition of double entry accounting and price ratio.
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