Mr. Yaron Brooks from the Ayn Rand Institute argues that global income inequality is decreasing. True/false?
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Here is a fairly instructive figure showing a cross-country measure of income inequality:
It shows that inequality was increasing for most of the last 35 years, but has started to decrease again recently. (You can read more at the source for this figure: http://www.conferenceboard.ca/hcp/hot-topics/worldinequality.aspx)
Once data is weighted by population, we see a longer-term trend for decreasing inequality (due to rapid growth in China and India, which contain around a third of the world's people:
As @FooBar notes in a comment, a pattern of decreasing income inequality is consistent with economic theories of convergence.