Money modelling

Read more: “The age of inequality: The 1 per cent and the rest”

“The 1 per cent” may be a catchy phrase, but when it comes to understanding how wealth is distributed within society, we should focus on the top 5 or 10 per cent. Those who study income distribution have discovered that there is one rule for the rich and one rule for everybody else. For the masses, income follows a broad curve; for the wealthiest 5 to 10 per cent, the pattern is different, forming the so-called Pareto tail (see graph).

The statistical pattern seems to be ubiquitous and unchanging – “from ancient Egypt up to today”, says Juan Ferrero, a physicist at the University of Córdoba in Argentina. That implies that there may be a universal mechanism at work.


More than 100 years ago, physicists pointed out that the broad income curve for the majority resembles the distribution of energy among molecules in a gas, a pattern called the Maxwell-Boltzmann distribution. This prompted the idea that the distribution arises because people exchange wealth when they meet, much as gas molecules exchange energy when they collide.

That idea has since been tested using mathematical models that liken human beings to molecules bouncing around in a gas. In the simplest model, people risk surrendering all their wealth at each encounter. That produces a wealth curve that has far more ultra-poor people than we find in the real world. So in 2000, Bikas Chakrabarti’s team at the Saha Institute of Nuclear Physics in Kolkata, India, allowed people to retain some of their wealth in each exchange. The result was a wealth curve similar to the broad hump of the Maxwell-Boltzmann distribution.

The next refinement was to allow different people to hold back different percentages of their wealth – effectively setting money aside as savings. With this tweak, the model correctly reproduced the whole wealth distribution curve, including the Pareto tail, which was made up largely of people who saved the most. This finding has been backed up by other similar models, including one developed by Ferrero, in which the richest 10 per cent are once again those most inclined to save.

If these simple models do capture something of the essence of real-world economics, then they offer some good news. It turns out that the main part of the wealth distribution gets narrower, more equal, the more people choose to save. In other words, inequality can’t be abolished, but it can be reduced if we all put more money aside for a rainy day.