Question

Name	Individual Income	Total Income	Income %	Population %
Jim	10,000	10,000	20%	50%
John	40,000	50,000	80%	100%

please find the gini coefficient for the Jim and John showing work

Answer 1

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There are only 2 people, Jim and John, so % of population is 0.5, Jim earns 10000 and John earns 40000, Total income = 50,000. So Jim's fraction of income = 10000/50000 = 0.2, John's fraction = 40,000/50,000 = 0.8.

Name	Fraction of income	Fraction of population	% of population that is richer	Score
Jim	0.2	0.5	0.5	0.3
John	0.8	0.5	0	0.4

Next we calculate the score

Score = Fraction of Income * (Fraction of Population + 2 * % of Population that is richer)

Score for Jim = 0.2* (0.5+ 2 *0.5) = 0.2 * 1.5 = 0.30

Score for John = 0.8 *(0.5+ 2*0) = 0.8*0.5 = 0.40

Adding the terms in the score column = 0.3 + 0.4 = 0.7

Gini coefficient = 1 - Sum of Score

Gini coefficient = 1 - 0.7 = 0.3

So Gini coefficient = 0.3