Equations !

Cool, I did a cut and paste from the Grumpy Economist and they work on my chrome browser. 

I will be constructing the quantum mechanical version of the fiscal price theory of the economy.  I make the Fisher equation my Hamiltonian and match that against an eigenvalue condition.  The eigenvalue condition make the government debt evaluation series  a finite, small rank (5) distribution channel with fixed and finite count of trades over the depreciation cycle of the spanning tree of deliveries. The finite polynomial is in algebraic on the trade book uncertainty at the retail point of delivery, where voters buys the local guv goodie. The vote turn around induces a fixed market uncertainty every where.  We have the complete sequence, and the window size will be restricted due to combinatorics before we even consider an economic law. The economic law is simple, at any equilibrium, voters everywhere wait in the same sized queue for guv goodie.

Sandboxers know this leads to rational approximation theory, thus Markov tree, thus the hyperbolic condition on indices. We are doing the constricted flow model of guv goodie. Along the distribution points agents adjust container size  such the spare capacity needed is bounded, uniform random. 

I have a bias, i guess the result.  U will find solutions but retail market uncertainty is huge. At the federal level, we are forced into huge containers. The window size is longer than the voter lives, and we always run imbalances greater than normal resulting in depressions on significant container size adjustment. I would find the same thing Roger Farmer found, people die sooner than they vote.

In the case of the USA the cause is the distribution imbalance due the malproportioned state system. We cannot afford the complex combinatorics.

fThe FTMP model 

(From here on in, the post uses Mathjax. It looks great under Chrome, but Safari is iffy. I think I hacked it to work, but if it's mangled, try a different browser. If anyone knows why Safari mangles mathjax and how to fix it let me know.) 

Here is the example. The model consists of the usual Fisher equation,$$i_t=r+E_t{\pi }_{t+1}$$and a Taylor-type interest rate rule$$i_t=r+\varphi {\pi }_t+v_t$$

$$v_t=\rho v_{t-1}+{\epsilon }_t^i$$

Now we add the government debt valuation equation$$\frac{B_{t-1}}{P_{t-1}}\left(E_t-E_{t-1}\right)\left(\frac{P_{t-1}}{P_t}\right)=\left(E_t-E_{t-1}\right)\sum _{j=0}^{\infty }\frac{1}{R^j}{s}_{t+j}$$

Linearizing$$\begin{array}{}{\pi }_{t+1}-E_t{\pi }_{t+1}=-\left(E_t-E_{t+1}\right)\sum _{j=0}^{\infty }\frac{1}{R^j}\frac{s_{t+j}}{b_t}=-{\epsilon }_{t+1}^s& \text{(1)}\end{array}$$with $b=B/P$. Eliminating the interest rate $i_t$, the equilibrium of this model is now$$\begin{array}{}{E}_t{\pi }_{t+1}=\varphi {\pi }_t+v_t& \text{(2)}\end{array}$$

$${\pi }_{t+1}-E_t{\pi }_{t+1}=-{\epsilon }_{t+1}^s$$

or, most simply, just$$\begin{array}{}{\pi }_{t+1}=\varphi {\pi }_t+v_t-{\epsilon }_{t+1}^s.& \text{(3)}\end{array}$$