Question

There are only three families living on an island. All of them are working and collaborating in producing the island's economy.
• Family 1 is the land owner consisting of a father and son. The monthly income of this family is $220
Family 2 is the island manager working for the land owner and managing workers in the island. The monthly income of this family is $60. The family consists of a father, mother and one child.
Family 3 is the worker on the island. The family receives a monthly income of $15 and consists of a father, mother and 3 children. It was announced that the monthly poverty line per capita of the island is $4.

a. Calculate the Gini ratio of the island.
b. Suppose the landowner family would like to make sure that the island's Gini is equal to 0 by donating some of the family's income to others. Would the landowner be able to do so? And if so, how much monthly funding does the landowner have to distribute to each family?

Answer 1

a. Calculation of Gini Ratio is as follows

Population	Income	Fraction of Population= Population/ Total Population	Fraction of Income= Income/ Total Income	Fraction of Richer Population	Score	Aggregate Score	Gini
5	15	0.5	0.05	0.5	0.08	0.37	0.63
3	60	0.3	0.20	0.2	0.14
2	220	0.2	0.75	0	0.15
10	295

1. Arrange the income level from smallest to largest.

2. Fraction of Richer Population = 1- 0.5 = 0.5

= 1- 0.5 - 0.3 = 0.2

= 1-.05 -0.3 - 0.2 = 0

3. Calulate Score = Fraction of Income *(Fraction of Population + 2* Fraction of Richer Population)

4. Aggregate Score is the sum of scores.

5. Gini = 1- Aggregate Score

b . Gini = zero implies income distribution is equal. If all the families on the island have the same income, then Gini will be zero. Given per capita poverty line income is $4.

The total income of the island is $295. The total population of the island is 10. Therefore, per capita income is 295/ 10 = $29.5

Population	Per capita Income	Income	Fraction of Population	Fraction of Income	Fraction of Richer Population	Score	Aggregate Score	Gini
2	29.5	59	0.2	0.20	0.8	0.36	1.00	0.00
3	29.5	88.5	0.3	0.30	0.5	0.39
5	29.5	147.5	0.5	0.50	0	0.25
10		295

The landowner would give 147.5 -15 = $132.5 to a family of 5 members and 88.5 - 60= $ 28.5 to a family of 3 members. The total income of the landowner would be 220 - 132.5 - 28.5 = $59.