Pareto's Law

Why it is hard to share the wealth
New Scientist - Jenny Hogan

The rich are getting richer while the poor remain poor. If you doubt it, ponder these numbers from the US, a country widely considered meritocratic, where talent and hard work are thought to be enough to propel anyone through the ranks of the rich. In 1979, the top 1% of the US population earned, on average, 33.1 times as much as the lowest 20%. In 2000, this multiplier had grown to 88.5. If inequality is growing in the US, what does this mean for other countries?

Almost certainly more of the same, if you believe physicists who are using new models based on simple physical laws to understand the distribution of wealth. Their studies indicate that inequality in market economies may be very hard to get rid of.

Pareto's law
In 1897, a Paris-born engineer named Vilfredo Pareto showed that the distribution of wealth in Europe followed a simple power-law pattern, which essentially meant that the extremely rich hogged most of a nation's wealth. Economists later realised that this law applied to just the very rich, and not necessarily to how wealth was distributed among the rest.

Now it seems that while the rich have Pareto's law to thank, the vast majority of people are governed by a completely different law. Physicist Victor Yakovenko of the University of Maryland in College Park, US, and his colleagues analysed income data from the US Internal Revenue Service from 1983 to 2001.

They found that while the income distribution among the super-wealthy - about 3% of the population - does follow Pareto's law, incomes for the remaining 97% fitted a different curve - one that also describes the spread of energies of atoms in a gas (see graphic).

Gas analogy
In the gas model, people exchange money in random interactions, much as atoms exchange energy when they collide. While economists' models traditionally regard humans as rational beings who always make intelligent decisions, econophysicists argue that in large systems the behaviour of each individual is influenced by so many factors that the net result is random, so it makes sense to treat people like atoms in a gas.

Class jumping
This, along with research data from other countries, suggests that there are two economic classes. In one, the rich grow richer while in the other the poor stay poor. Yakovenko explains this by going back to the analogy of atoms in a gas.

The atoms assume an exponential distribution of energy when they are in thermal equilibrium, and pushing the gas away from this state takes a lot of energy and it could prove similarly difficult to shift an economy to a different state. Randomness in the model does, however, mean that individuals can jump from one class to another.

"It suggests that any kind of policy will be very inefficient," says Yakovenko. It would be very difficult to impose a policy to redistribute wealth "short of getting Stalin", says Yakovenko.
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(It might be better to instate a "Pareto´s Tax" instead of a new Stalin*)

World's economies show similarities in economic inequality
PhysOrg - Lisa Zyga
Economists who yearn for the redistribution of wealth in an ideal society are up against history. According to a recent study, the uneven distribution of wealth in a society appears to be a universal law that holds true for economies in many different societies, from ancient Egypt to modern Japan and the U.S. This distribution may reflect a simple natural law analogous to a 100-year-old theory describing the distribution of energy in a gas.
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