Let's derive the money equation from the supply/demand equation

We will solve this for the normalized symmetric case, the case when prices and supply make a symmetrical V at equilibrium.  And we are going to normalize it so gains are always one unit of currency.  Then extend it to a connected distribution network.

First, we let prices decay by some rate as supply grows by the same rate, and we set the quantity levels to normalize.
We have:

(1+1/r) growth rate of supply, and (1-1/r) decay rate for price.  Then the normalizing quantity basis is r so that:

(1+1/r)^2 - (1-1/r)^2  =4/r

I think I have that right .  The square ensures equilibrium because it projects the gain out two periods. Hence there will be two transaction available to realize the projections and with probability one the queue length for all transactions will be less than three.  The Nyquist bandwidth requirement is met, and that is the condition of an adapted process.

Now one should always be able to do this if the real quantities and rate are known and independent, there are enough variables to normalize.

But we can see I have constructed the problem as a unitized, symmetric hyperbolic condition.  Hence the differential equation of flow is satisfied.

Let price be  (1-1/r)/1+1/r), the ratio of price to supply in the current quater.  The that is tanh and we get inflation right away as tanh'. So then computing or measuring tahn'' we get the money equation:

Price * Inflation +1/2 Inflation' = 0.

If we require a connected network where all quantities are conserved, then r will always be of the form 1/Phi^(2n), where n enumerates the node level of the distribution network.

I think I have all that, if not, economists can work it out before they teach it.  The symmetric case is the first Lagrange. The asymmetric cases that use higher Lagrange numbers will require less inflation', the higher Lagrange numbers assume all the Phi estimates have been consumed. I am still working that one out.

This helps explain why Dean Baker's logic on inflation and inflation rate of change is a bit wrong. His theory is that inflation and inflation rate of change can be set independently, and we see they are mutually constrained by the price level.

But what this all means is that I have two chances to get to my favorite restaurant for apple  pie, and that should be enough to prevent crowd.

Here by the way is the connection between hyperbolics and Lagrange.

  One can see this form closely related to the equation above. The variable r is a quadratic surd, but it determines 1/r *  tanh'' where 1/r is 1/2 when the symmetric hyperbolic is used.  Otherwise much remains the same, but there is certainly a bit of work for mathematicians to formally redo Lagrange theory in generalize hyperbolics.  Followign the link we see all the connections between hyperbolics and Marks bringing us to Weiner and Brownian motion then Schramm-Loewner.   

It is the calculus of combinatorice, a Schur reduction of chaos into optimal sets up to a standard error. Raising the lagrange order move the spectral peak down to a different angle and decomposis the tanh curve with another basis set. The theory of everything, actually.

Derive the whole mess from discrete angle hyperbolics and be done with it.