# The Chilling Effect of Inflation

There has been some discussion in the news about inflation. Japan is actively pursuing inflationary policy with the Yen. The Federal Reserve is not backing off of its Quantitative Easing, taper-off. Meanwhile, India is is watching their currency collapse. And the ECB just announced a surprise lowering of their interest rates. One of the hallmarks of modern economic theory is the stimulatory nature of increasing consumption now. This is financed through two mechanisms, debt and increasing the monetary base. The root of the dual mandate of the Federal Reserve is that inflation as shown by the Phillips Curve causes higher employment. This is dangerous policy. Here is the math explaining why.

Using a simple Cobb-Douglas economy where we have four exogenous variables, utility $U$, quantity of money $M$, number of people in the workforce $N$, and some defined economic structure measured by entropy $S$:

$S=N_i\,s_0+N_i\,\mathrm{Log}\left[\left(\frac{U}{U_0}\right)^c\left(\frac{M}{M_0}\right)\left(\frac{N_i}{N_{i,0}}\right)^{-(c+1)}\right]$           (1)

We assume the Phillips curve relationship follows a power law of the form with $a>0$:

$\left(\frac{N}{N_0}\right)=\left(\frac{\lambda_0}{\lambda}\right)^a$      (2)

Recalling $\frac{\partial S}{\partial M}=\frac{\lambda}{T}$, we find

$\lambda M= N T$      (3)

Using the relationships (2) and (3) in (1) and assuming the process is isentropic (no structural changes within the economy) we find

$\left(\frac{T}{T_0}\right)^{c+1}=\left(\frac{\lambda}{\lambda_0}\right) e^{-\left(s_0-\left(s_0+1\right)\left(\frac{\lambda}{\lambda_0}\right)^a\right)}$           (4)

The result shows that if our economy follows the Phillips curve, our economic activity, $T$, is reduced. This requires a coordinated policy to devalue the currency. Such action reduces the economic activity.  The dual mandate of the Federal Reserve, to ensure economic stability and a targeted inflation causes the economic activity of the country to be lower.  Our economy cools.

Using the velocity of money as a proxy for economic temperature we find that as the Fed implemented QE-ternity, that yes indeed the Phillips curve held and the economy cooled.  Thank you Federal Reserve and the United States Government for making us all worse off.  This effect is not just here in the US it is in the entire world.

If there are structural changes in the economy, the relationship does not hold as the process is no longer isentropic, here we need more information to assess the thermodynamic path of the economy.  Over the long term cooling of economic activity will result in structural changes within the economy. We can expect that under the existing constraints the entropy of the economies will reduce. Reduced entropy destabilizes the overall system and can lead to bifurcation (revolution). While it may be hard for the central banks and various governments to act responsibly if they do not do so, they will eventually set in motion their own destruction.

“Entropy always wins” -Jeff Terry

“If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” -Sir Arthur Eddington

Update: To make things a little more clear as to how I got to my conclusion about printing money is to plug 4 and 2 into 3

$\left(\frac{\lambda}{\lambda_0}\right) \left(\frac{M}{M_0}\right)= \left(\frac{N}{N_0}\right) \left(\frac{T}{T_0}\right)$

$\left(\frac{M}{M_0}\right)=\left(\frac{\lambda}{\lambda_0}\right) ^{1/(c+1)-(a+1)}e^{-\frac{\left(s_0-\left(s_0+1\right)\left(\frac{\lambda}{\lambda_0}\right)^a\right)}{c+1}}$

This shows how as money is printed the marginal utility of money, $\lambda$ goes down.  This is for a Cobb-Douglass economy, that does not have structural changes, and follows a Phillips curve.