Robert T. Jantzen and
Klaus Volpert,
“On the Mathematics of Income Inequality: Splitting the Gini Index in Two”,
The American Mathematical Monthly,
119 (2012), no. 10, 824 - 837.
This article starts with the stunning fact that a certain hedge fund manager earned more in 2010 than 50,000 math professors combined. Followed by a graph showing us the percent of annual national income received by the top 1% of wage earners since 1913, this paper easily entrances the reader into exploring various measurements and characteristics of income inequality.
Using concrete examples, the authors give clear definitions of Lorenz curves and the Gini index. This index is a number that gives an indication of income inequality in an economy, but its computation requires more information than would normally be available from government sources. The authors use the 2009 U.S. quintile income data to show the challenge of modeling, in a valid and meaningful way, this economic situation with the incomplete data.
Going back and forth between economic examples and mathematical models, we are led to a Lorenz curve that both fits the data plus uses meaningful parameters. Most of this is done using just our knowledge of functions and their integrals, yet there is enough mathematical rigor and economic data that we have the double pleasure of investigating a mathematical concept in depth and feeling we are keeping on top of current events.
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