Wealth always trickles up – it’s all in the maths

I bumped into a very interesting article in the ‘Scientific American’ – which I confess is not my usual bed-time reading and whose maths I find sometimes fairly challenging….

But nonetheless, by using ‘agent-based models’ (indeed they could even be called free agents) a team were able to replicate equal exchanges within an economy and discover that those that win the first 50:50 ‘coin toss’ exchange the first few times begin to destablise the ‘fairness’ of the economy, and that this instability gets gradually amplified, the trickle up gradually becomes a flood and wealth concentrates into an oligarchy.

The piece asks:

Does this mean that poorer agents never win or that richer agents never lose? Certainly not. Once again, the setup resembles a casino—you win some and you lose some, but the longer you stay in the casino, the more likely you are to lose. The free market is essentially a casino that you can never leave. When the trickle of wealth described earlier, flowing from poor to rich in each transaction, is multiplied by 7.7 billion people in the world conducting countless transactions every year, the trickle becomes a torrent. Inequality inevitably grows more pronounced because of the collective effects of enormous numbers of seemingly innocuous but subtly biased transactions.

What the author describes as a ‘quirk of arithmetic’ means that taxes are essential to avoid oligarchy (as well as inflation)! Indeed the researchers model for a wealth tax and a subsidy for the poor – both of which were demonstated to counteract the concentration effect and make for a stable economy. They demonstrate too, that without these measures an oligarchy is mathematically inevitable. So instability is inherent to any economy operating without properly compensating taxation.

Indeed this whole analysis recalls and reinforces the study from the University of Catania suggesting that meritocracy was decidedly suspect.

The article concludes in a devastating conclusion for ‘equilibrium economics’ as well as ‘free’ markets:

We find it noteworthy that the best-fitting model for empirical wealth distribution discovered so far is one that would be completely unstable without redistribution rather than one based on a supposed equilibrium of market forces. In fact, these mathematical models demonstrate that far from wealth trickling down to the poor, the natural inclination of wealth is to flow upward, so that the “natural” wealth distribution in a free-market economy is one of complete oligarchy. It is only redistribution that sets limits on inequality.


  1. Chris B -

    How rewarding to find mathematical proof of something we all knew.

    1. Peter May -

      Agreed – and I was pretty surprised to discover it!

  2. Neil -

    Thank you, Peter, for highlighting a most interesting article. Society would be better off if we could take this to heart: “Luck plays a much more important role than it is usually accorded, so that the virtue commonly attributed to wealth in modern society—and, likewise, the stigma attributed to poverty—is completely unjustified.”

    Economists do like models, but will this one gain acceptance and shape policy? One can only hope.

  3. B Gray -

    Thanks for sharing this article. It dovetails nicely with some research done at the University of Maryland back in 2014 to mathematically model the collapse of societies. It used a variant of the predator-prey population model (Human Nature and Dynamics or HANDY) to model the carrying capacity of the environment relative to population growth, resource depletion rates, and economic stratification of society. Model uses society as the “predator” and the environment/natural resources as the “prey”.

    Conclusion is over-exploitation of resources and strong economic stratification can independently lead to complete irreversible societal collapse. In fact at the current levels of inequality we see today, all of the models invariably lead to collapse.

    Link to the paper if you are interested:

Comments are closed.