Yesterday I listened to a talk by Victor Yakovenko of the University of Maryland about the physics of money and it was quite interesting. I think that after this talk I am finally beginning to understand economics while at the same time I suspect that most economists don't.
In his talk he said that back in 2000 he published a paper on how to apply statistical mechanics to free market economics. He did it as a hobby and did not consider it to be very important, meaning he still did his normal research involving condensed matter physics. A few years later he realized that his paper on the statistical mechanics of money was getting more citations than any of his other papers, so he switched his focus of research to Econophysics.
One of the most interesting results that he found was that in a free (random) system of monetary exchanges the natural distribution of money will converge, over time, on a Boltzmann-Gibbs distribution. The argument is simple. In stat mech you have a system where small, discreet amounts of energy are passed from one particle to another. This system leads to a probability distribution characterized by the equation [all images come from Dr. Yakovenko unless otherwise stated]:
This problem was solved in 2005 by Xi, Ding and Wang when they considered the effect of the Required Reserve Ratio (RRR), which to explain simply limits the amount of money that lenders can lend. In terms of the simulations this means that every time someone goes into debt the corresponding positive money that is created cannot all be used to finance more debt. A certain amount must be held in reserve. This limits the total debt that can be issued by the system based on the total amount of money that was in the system to begin with. The end effect is that the distribution becomes something like this [From Xi, Ding and Wang]:
Now let's look at some real data. Using US census data from 1996 they plotted income and found that it fits nicely to a Boltzmann distribution, as long at you do not get too close to $0 (above $10,000 works fine).
Pareto power law distribution.
So what happens when this distribution gets upset by programs such as social welfare or other effects. In a paper published in 2006, Banerjee, Yakovenko, and Di Matteo give the following graph showing the distribution of income in Australia.
When asked about the predictive power of this his response was, "None." He explained that this data takes a long time to collect and to analyze, which creates a lag of several years in the data. But by the time the data has been collected and analyzed and we are able to see a bubble (like the housing bubble) the bubble has already burst and we have moved on. But this also means that modern free market economics behaves in a very statistical manner and can thus be controlled (in theory), which is what the Fed is currently trying to do. Dr. Yakovenko did not get too much into the politics of it, but he did make it clear that he did not agree with the way the bailouts were handled, and the current tactic of the Fed. But it was also clear that he preferred a free market, though a heavily regulated one. He was also very concerned about the inequality in the system, and noted the existence of two classes of people and made reference to Karl Marx at that point.
On the whole I was rather impressed with what he was doing and like I said, I think I am finally beginning to understand economics. Someone just had to explain it to me in terms of physics and it made perfect sense.
XI, N., DING, N., & WANG, Y. (2005). How required reserve ratio affects distribution and velocity of money☆ Physica A: Statistical Mechanics and its Applications, 357 (3-4), 543-555 DOI: 10.1016/j.physa.2005.04.014