Using simulation to explain the Wealth Gap in the world

Picture of chess set showing inequality

The rich keep getting richer, and the poor keep getting poorer as the saying goes. But why is this true? What factors are in play keeping this inequality in existence, and why can’t ordinary people or even governments do anything to stop this?

These questions have bothered Dr. Alan Barnard, of Goldratt Research Labs, for many years. He has identified different conditions that play a role in whether someone becomes a top earner, perhaps one of the richest people in the world, or simply an average earner, like the vast majority of people. These are known as success conditions and fall into those either in or out of our control. Hard work and good decisions, including hell-no decisions, are in our control, whereas good genes and good luck are not.

For his presentation at the AnyLogic Conference 2021, Dr. Barnard identified luck as a key component in determining wealth and the widening wealth gap. He was intent on showing this through the use of simulation and built a model using an in-house developed Material Design Library and AnyLogic simulation software. This software could replicate real-world complexity through agent-based and discrete-event simulation methods.

The Village Experiment

In the model scenario, a village of 100 people existed. Each person started off with a personal wealth of $100. They then traded with each other for 100 days, and with each trade there was a 50-50 chance of winning. If they won, they would win 20% of their wealth, and if they lost, they would lose 20% of their wealth. So, after 100 days what happened with the distribution of wealth?

The first time the model was run with the parameters set in the illustration below. The results of the model showed that the poorest trader had a wealth of $0.07, and the richest trader had a wealth of $1,700 – a difference of over 25,000 times. At the same time, the Gini coefficient was 0.82. What happened? Well, the richest person was simply luckier than all the rest. This person had about 63% wins, while the poorest had only about 37%.

First experiment parameters and results

Model showing the parameters to set, for the first experiment, on the left, and the results illustrated on the right (click to enlarge)

It’s easy to understand that with the most wins, you would be the richest, and with the least wins, you would be the poorest, but what is not so easy to understand is what happened to those with a 50-50-win rate. Well, they actually ended up with only about $13. It seems counter-intuitive, but it’s true. You might wonder – how can you win 50% of the time and yet still lose $87? Let's check - if you start with $100 and you win 20%, you will have $120; but if you then lose 20%, you will only have $96. Continue this for some time and you could end up with $13.

So, how about if the scenario was altered and some help was given to those poorest people. There is such a thing as a wealth tax, and this could be applied on the richest and redistributed to the poorest.

The second simulation, illustrated below, was run with a 20% wealth tax, and an 80% tax reinvestment rate with the poorest 20% being eligible. Did this help? Did this offset the apparent lack of luck the poorest people had? The results would seem to indicate that it did help. The richest trader had $519.13, while the poorest trader had $52.13 – a difference of only 10 times, while the Gini coefficient was 0.26. This is a significant improvement for the poorest trader and represents a smaller wealth gap.

Second experiment parameters and results

Model showing the parameters to set, for the second experiment, on the left including a wealth tax and tax redistribution, and the results illustrated on the right (click to enlarge)

See the simulation in action below:

The wealth gap simulation

However, at the end of the day, even with government intervention, there is still a large and growing wealth gap. Therefore, it is important for governments and decision makers to understand that there needs to be another mechanism to prevent hard working people from ending up with only $13 from their hard-earned $100.

New Insights

One more insight that was gained from this simulation – how much “good luck” does someone need to grow wealth? Let’s look at another of his examples. You have $100, and you have the option to play a game where a win gives you 30% and a loss gives you 25%. This seems like a game that would be in your favor. But, thinking back to the previous situation we can understand that this will probably result in a loss even though the odds look good. And yes, after 20 "better-than-fair" trades (win, loss, win, loss…), you would have lost almost 22% of your wealth. So, the question remains, how to grow your wealth?

What should be the gain% to at least break even? Again, Dr. Barnard found an answer, and he came up with the following formula:

Gain% = Loss% / (1 – Loss%)

If you know the loss percentage, you can work out what gain you need to counter it. For example, if you have a loss% of 10%, your breakeven gain would be 11%; for a 25% loss you would need to have a 33% gain; and for a 50% loss, a 100% gain is necessary. As the losses increase, the amount needed to break even increases.

Rich or poor

Knowing all this is well and good, but in a complex system with uncertainty, it is very easy to make bad decisions and very hard to learn from these. So, as with all challenges, come opportunities. The opportunity here is to make it harder to make bad decisions, and also then make it easier to learn from bad decisions if you happen to make them.

One of the best ways to do this, is to use simulation. Simulation can predict the range of impacts, test which strategy is best for the system, or test hypothesis of consequences. Finally, just think of every change/decision as an experiment to learn from and you will be headed in the right direction.

So, can we all end up like Elon Musk or Jeff Bezos? Well with hard work, good decision-making, probably having good genes, and a little bit of luck – maybe (or maybe not). But there is definitely no harm in trying.

This model was presented by Dr. Alan Barnard, CEO, Goldratt Research Labs, at the AnyLogic Conference 2021.

The slides are available as a PDF.

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