First, let see what the exact fiat banker equation looks like.
Let g be prices received plus deposit rate on money; divided by prices paid plus lending rate on money. Then gain, g, is the ratio of input and output costs, including prices implicitly. g', the first difference is the change in gain. So a change in economic gains includes the change in prices. The second difference , g'', tell you how fast the economy adapts. The equation:
g * g' = 1/2 * g'', means everyone can get their price changes done on time. The 1/2 appears because g'' as known to half the certainty of g'.
For an economy with a fixed structure, g'', the second difference is a constant for each type of business, including the fiat banker. It varies among the types of business, but remains constant for each type.
So the fiat banker can only put out a fixed quantity of money each rate period, an absolute count of dollars. The fiat banker performs the same simple operation every planning cycle. It sets the deposit rate and lending rate so the money in and out, including principal, is equal to the constant dollars it can safely deliver. That is, savings,S, and lending,L, compounded to the next cycle:
S^2 - L^2 = constant,
The planning cycle is one half the time to collect the second differences, that is the optimum information period for the fiat banker, the Shannon Nyquist rate.
The fiat banker assumes the lenders and savers take their money out or return lent money over the fiat bankers planning cycle. It computes projected net flow compounded to the next period, including principal. That is all it can do and it is sufficient for price neutral growth. It is sufficient because companies seeing sudden growth will move more money into the economy by puting their gains on deposit to earn rates. They surprise the fiat banker into emitting more rates paid out, via the deposit system, free unencumbered cash. So price neutrality is automatic.
A well functioning fiat system will always have price neutral growth.
So where did the inflation come from?
I didn't, it has become deflation and the retail banking sector is drying up. Rates are low, prices dropping, and all the fractional reserve money is winding back to the Fed. The force of interest payments on debt is appearing and causing the fiat system to unwind. It is simply a matter of understanding the long sample period make equilibrium a long process. The cause of the long period, obviously, are the politicians in DC, and their probability distribution goes out to the entitlement spending period, 30 years.
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