Baumol-Tobin won't work

Baumol-Tobin is Magic Walrus.

This model assumes a consumer has a regular income and pays regular payments, thus the consumer deposit/loan functions can be differentiated. Terms are pre-defined, not just sarse, but already known.

Basket brigade assumes the consumer makes ad hoc re-orderings of the purchases to avoid local congestion.  The consumer accepts that the cost of money is uncertain, but bounded within the household budget. It can re-order purchases without being surprised at the credit card charges.

Thus, the optimum loan to deposit functions= will tend to match the size and relative frequency of liquidity events to the size and relative frequency of deliveries. We get a sparse pricing system that obeys Baumol-Tobin over a sub set of all real prices.

This came up in the Alt-M blog on IOER again, and the problem with IOER is the denominator, time.  The way to eliminate time is relatively simple, mechanically.  Just move to an asynchronous, adjustable interest rate, which is equivalent to open market buying and selling of fiat. The central banker can determine the earnings from deposits and costs of loans on the spot, as needed, and it keeps a balance sheet equal to the expected round off error.

All parties are operating from and expected, but bounded uncertainty, tradebook uncertainty. Brigade theory applies.