Advancing the theory a bit

Stolen chart from Mathworld

Computing the Fibonacci numbers, when bandwidth are varies around the value x=1

Let me take for granted the Fibonacci series is what we want for determining the equilibrium transaction rates along any yield curve constructed of minimal redundancy production networks.  The equation above are the Fibonacci polynomials which compute to the Fibonacci series when x = 1.  Hence, the Nth Fibonacci number is Fn(1.0).  Transaction rates along the curve would be given by:  F3(1.0), F4(1.0),...

Bankers do not use the formula above, instead they use this one: Fn(b) = x*Fn-1(b) +  Fn-2(b).  This means that the rates at one term are really determined by the rates at the two longer terms above.  The banker can work the problem from the short end or the long, it depends on where the constraints are.  And, we should be dealing with transaction rates, not term periods.

The advantage in our case is, though I say that without proof at the moment, we can treat x as the basic bandwidth of the system.  So then when production slows when x, the bandwidth, slows. We can recompute the nearest optimum set of transaction rates, while off equilibrium, by setting x off unity by a bit.  This is great news, and I am playing with off equilibrium yield curves, like the one we had in Fed 2006, and I think this method will track the performance we saw.

Here are some yield curves at different bandwidth.  Remember that these curves are relative to current equilibrium, when bandwidth = 1.0.  Scales are constant but not calibrates to the real economy.

 Economic bandwidth is below equilibrium

 The economic bandwidth at equilibrium

 The economic bandwidth above equilibrium.

The key variable is bandwidth relative to equilibrium.  Currently we are pushing bandwidth above its equilibrium  point, QE2,  but the economy has already dropped rank

Warning! I often gets things off a little when working right onto the web, but this is my current best.