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Gini Coefficient: Understanding how to measure income inequality

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Gini Coefficient: Understanding how to measure income inequality.

There are three social classes (within each social class, income is equally distributed) and their population share, and total income share are given as follows:

If you prefer a function rather than a table, use the information below where x is the accumulated percentage of population in the country and f(x) is the accumulated percentage of income:

• Poor: f(x) = 0.2x, if 0≤x≤0.5
• Middle: f(x) = 0.1 + 1(x-0.5), if 0.5≤x≤0.9
• Rich: f(x) = 0.5 + 5(x-0.9), if 0.9≤x≤1

1. Draw the Lorenz Curve and shade the area of inequality (i.e., compare it to the egalitarian distribution of income).

2. Calculate Gini coefficient of this society.

3. [Bonus: 5 points] Calculate the new Gini coefficient if the government imposes a 20% income tax on rich people (i.e., collect 20% of the income of the rich) and then redistributes all the tax revenue to the poor people?