Ich denke einige im Forum kennen das vielleicht nicht, wir hatten dazu bereits vor 2-3 Jahren eine umfangreiche Diskussion zu dem Thema

Kurz: Reichtumskonzentration ist ein "natürlicher Prozess"
verursacht durch das Wirken des Zufalls.

Hier das Modell
http://www.dasgelbeforum.net/forum_entry.php?id=257875

Hier reale Daten und Vergleich mit Simulation
http://www.dasgelbeforum.net/forum_entry.php?id=282975
http://www.dasgelbeforum.net/forum_entry.php?id=282976

Mehr dazu in den betreffenden Threads. Wer sich noch mehr für Details interessieren sollte, hier ist noch etwas, was ich mal jemandem per Mail dazu erläutert hatte, sorry dass es in englisch ist, möchte es jetzt aber nicht erst übersetzen, daraus "inequality grows also here unlimited with time".

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I'm not an economist, however 2 years ago I was thinking about the causes of the wealth distribution and looked for economic theories and was surprised that what I think is one of the main reasons was not even mentioned in economic theories.

In the Solow-Swan model it is shown mathematically that it comes to convergence of wealth, but that's not what one can see in the real world.

Did economists consider that the influence of randomnes could be the reason for this?

A few examples:

2 farmers (with same capital and larbour) grow potatoes,
one yields 500 units (because of bad weather), the other 1500 units (good weather).

2 used car dealers buy each the same type of used car for 10000 units.
One of them is lucky and sells it already the next week for 12000 units.
The other one isn't ale to sell it, finally sells it after one year for 8000 units.

2 rich guys A and B buy stocks.
A buys stocks of company X for 1000 units.
B buys stocks of company Y for 1000 units.
After one year the price of stock X is 500 units, the price of stock Y is 2000 units.

2 authors spend each a year to write a book and after that publish it.
One author sells 10 million copies of his book.
The other one sells 10 books.

Did economists consider that a function

y = w * l + r * k

does not reflect reality but should be replaced by

y = (w * l + r * k) * z

where z is a random variable and approx. 1?

I made a simple simulation
http://www.lutanho.net/trading/wirtschaftskreislauf.html
(currently only in german, in case there is interest, I could translate it and explain a little more)
with only a few parameters and with this I get the approx. log-normal distribution of wealth and I also get that the inequality grows over time as observed.

Real data: (source: http://www.jjahnke.net/wb/wb159-180413-9357.pdf)
Top 10: 58%
(Average: 195.200 Euro =100%)
Median 51.400 Euro =26.33%
73% of population have less then average of wealth

Simulation:
Top 10: 58%
(Average=100%)
Median=25% (shown when mouse pointer is over red line)
76% of population have less then average of wealth

Also the following real data are in accordance with the simulation:

year: 1998 2003 2008 2013
perc: 45 % 49 % 53 % 58 % (percentage of wealth of the top 10% welthiest in Germany)
sources:
http://www.spiegel.de/politik/deutschland/was-steinbrueck-und-merkel-ueber-die-einkomme... (1998, 2003, 2008)
http://www.jjahnke.net/wb/wb159-180413-9357.pdf (2013)

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Just some math about the unlimited wealth inequality growth which can be shown easily:

Additive shocks

W(i,t+1)=W(i,t)+z (W=wealth, i=index of agent, t=time, z=random variable)

result in a normal distribution of W

This follows from the Central limit theorem
http://en.wikipedia.org/wiki/Central_limit_theorem

Interestingly, the standard deviaton is proportional to square root of t,
this means when t goes to infinity, then also the standard deviation (~inequality) goes to infinity, but slower with growing time.

When there are multiplicative shocks

W(i,t+1)=W(i,t)*z (W=wealth, i=index of agent, t=time, 0<z=random variable)

then this leads to a log-normal distributuion, from the same wiki page:

"The logarithm of a product is simply the sum of the logarithms of the factors. Therefore when the logarithm of a product of random variables that take only positive values approaches a normal distribution, the product itself approaches a log-normal distribution."

So the multiplicative shocks produce a log-normal distribution and (because it is only a transformation of the additive case) the inequality grows also here unlimited with time.

But fortunatelly there is tax redistribution which drags the distribution in the other direction and there is also limited life span and inheritance.

I already modelled the inheritance of wealth in another simulation:
http://www.lutanho.net/trading/populationskreislauf.html
Model assumption is: Wealth is constant over life time, distribution of number of children is constant either 2, 1-2-3, or 0-1-2-3-4, wealth and number of children is uncorrelated.
Then the model with constant 2 children leads to equality of wealth, the other 2 cases lead to a log-normal distribution, but interestingly this time the log-normal distribution has limited inequality.

So when considering multiplicative shocks + inheritance of wealth this leads also to approx. log-normal distribution with limited inequality because the influence of the inheritance of wealth to the children drags the distribution back in direction of less inequality.

Some questions worth to investigate:
Where will be the steady state (depending on tax regime) and will the society still be stable there (considering the conditions in Greece and Spain right now)?
Is there a (mathematical sound) "optimum" (steady-state-) wealth distribution that should be tried to reach?