Question

Consider a community with ten persons.

a. Plot the Lorenz curve for the income distribution (2,2,4,6,8,20,30,40,60,100)

b. Consider an income redistribution that takes 20% of income from each of the three richest individuals and distribute equally to individuals that have an income below the poverty line(9). Plot the Lorenz curve again to demonstrate that inequality has decreased.

c) Show on the same diagram the Lorenz curve for the income distribution (8,18,20,22,26,28,30,32,40,48)

Answer 1

This is the first Lorenz curve.

Now 20% of income from 3 richest is distributed equally to people below the poverty line.

Contribution from the richest individual with 100 income will provide 20% of 100 = 20.

New income

=100 - 20 = 80

The individual with 60 income will provide 20% of 60 = 12

New income

=60-12 = 48

The individual with 40 income will provide 20% of 40 = 8

New income

=40 - 8

32

Total = 20 +12 + 8 = 40

This will be redistributed to people below poverty line i.e 9. There are 5 people with less than 9 income and 40 will be redistributed as 8 per person.

New Income Distribution

(10,10,12,14,16,20,30,32,48,80)

Its Lorenz curve is as follows

Lorenz curve for (8,18,20,22,26,28,30,32,40,48) is as follows

The Income here is better distributed, this can be seen by the area between the line of equality( blue line) and Income line(red line). Total income here is 272 just like in previous case but here, income is better distributed.