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The gini index measures how income is distributed in an economy. If your country has an index of 0, you're communist. If it has one of 100, you live in a house with other folks who are unemployed and there is only 1 bread winner. That's the simplest I can explain it.
Yes, the Gini index measures the concentration of wealth in a country. For example, it is well known that in Brazil the disparity of wealth between the rich and poor is enormous, very few rich people concentrate a huge portion of the country's wealth (for example Brazil's Elites Fly Above Their Fears (washingtonpost.com) (http://www.washingtonpost.com/ac2/wp-dyn/A42332-2002May31 - broken link)). Same for Mexico where you have for example Carlos Slim, either the wealthiest or one of the wealthiest men in the world in a country were a huge percentage live in extreme poverty.
So as the grpah explains, the closer the curve to the top of the graph the greater the wealth concentration.
In the US we have a lot of billionaires and thousands of millionaries but we do have a huge middle class what makes the index value lower, so the curve is around 50, although you can clearly see it trending upwards, indicating that the money is flowing to fewer hands than before.
The opposite occurs in France which has a socialist government for a number of years now. The index curve is going down indicating that the wealth is distributed more uniformly among the population than before. Norway has the same pattern.
Former communist countries like China and Bulgaria once they accept the capitalist model in the 90's start going up.
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