Problem : If there are only five people in a certain economy, and their weekly paychecks are $100, $300, $600, $1000, and $1600, what is the cumulative percentage of income generated by the bottom 60% of wage earners?The cumulative percentage is the amount of money earned by the bottom three workers (60% of the workforce), divided by the total income earned by all workers:
Bottom three income = 100 + 300 + 600 = 1000
Total income = 100 + 300 + 600 + 1000 + 1600 = 3600
Cumulative percentage income earned by bottom 60% = 1000/3600 = 27.8%
Problem : How is the Lorenz curve used to generate a numerical representation of income inequality?The Lorenz curve plots out the cumulative percentage of income earned by segments of the workforce, as compared to a perfectly even income distribution. By dividing the area between the two curves by the total area under the flat curve (which represents equal distribution), we generate the Gini coefficient, a numeric representation of income inequality.
Problem : If the area between an economy's Lorenz curve and the straight-line equal distribution curve is 2 units, and the area beneath the Lorenz curve is 4 units, what is the Gini coefficient for this economy?The Gini coefficient is the area between the Lorenz curve and the equal distribution curve divided by the entire area underneath the equal distribution curve. In this case, that would be equal to 2/(2+4) = 0.33
Problem : Why does an economy with a higher Gini coefficient have a less equal income distribution?Because the Gini coefficient is directly related to the area between the Lorenz curve and the equal distribution curve, the larger the Gini coefficient, the farther the economy deviates from a perfectly equal income distribution.