Question

Imagine that we start with the distribution of income. They are the following: 8,000, 22,000, 45,000,...

Imagine that we start with the distribution of income. They are the following: 8,000, 22,000, 45,000, 85,000, 11,000, 35,000, 115,000, 40,000, 37,000, 28,000.

A. Calculate gini coefficient

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Answer #1

The Gini coefficient is 0.384

First use the given formula

Here n = 10, i = 1 to 10 and yi is the income of the ith individual/group

In the table below, (n+1-i)*yi is calculated and a summation is taken out which is equal to 1526000. Summation of yi is 426000. Using these values we have

G = (1/10)*(10 + 1 - 2*(1526000/426000)) = 0.384

i yi (n+1-i)*yi
1 8000 80000
2 11000 99000
3 22000 176000
4 28000 196000
5 35000 210000
6 37000 185000
7 40000 160000
8 45000 135000
9 85000 170000
10 115000 115000
Sum 426000 1526000
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