Here is what I mean about banker bot

Go to the equation based on simple interest:

D*(1+d)^2 - L*(1+l)^2 = 1

Deposit liabilities and loan assets, projected two periods,  difference to 1.  What is that 1? This is all coming to me as I work it.  That 1 is the uncertainty of the member banks, it is the unit of uncertainty.  It has to be that way because the model assume money measures, so money has to have the fundamental unit of variance, and it is standardized to 1. So this equation is at equilibrium and the ratio:

D*(1+d)/L*(1+l) is tanh(a), a being the accumulation rate which includes principal and interest. This is me learning how it works. So now I am working on some of the dynamics in this simple model. But, notice that having converted to simple interest, one can change the frame work and have higher or lower loan rates compared to deposit rates. The frame depends on how one constructs who is depositing and who is lending along the chain. So re-arranging lending and depositing in groups as you wish, find the hyperbolic condition and exchanging assets and liabilities.

Here is a difficult read:

http://www.scholarpedia.org/article/Hyperbolic_dynamics#Introduction

I am plowing through this as we speak.

The game I am playing on my spread sheet is simple, any banker creates loans partly from the deposits and partly by borrowing at the wholesale market.  The ratios are set to conserve flow, that is using  ratios that map deposits into loans and maintain network additivity.  If the demand for loans increases then the central banker raises deposit rates, which partitions money demand better, and maintains flow.  That shows up as a loss on the currency bankers balance, and the loss goes to zero at equilibrium and the new money stays in the economy. If the economy slows a bit the currency banker decreases loan rates and earns more money in rates, taking the money permanently from the economy. Prices are stable as long as the network is adiabatic, it does not change structure. Wait, lowering rates earns money?  Dunno yet.

Central banking as we know it is not the model.

The central banker, today, has one member bank operating way out of equilibrium, so the central banker is shoved way off to a boundary condition.  Most federal reserve members know this. Normally the currency banker should be on top of a very sloped mountain, running from side to side with rate changes on deposits and loans of short periods to stay in the center, a fast paced business.  Currently Janet does a bit of this with her portfolio, but she is acting as if there were only one member bank.