Question

Given the data {20, 20, 30, 30, 40, 40, 50, 50, 60, 60}, calculate

1. Gini coefficient using the quintile distribution.

2. Draw the Lorenz curve with proper labels.

Answer 1

Total income is 400. We find that there are 5 quintiles and for each of them, the percentage of income is computed as

1st quintile: (20 + 20) = 40*100/400 = 10%. 2nd quintile: (30 + 30) = 60*100/400 = 15%. 3rd quintile: (40 + 40) = 80*100/400 = 20%. 4th quintile: (50 + 50) = 1000*100/400 = 25%. 5th quintile: (60 + 60) = 120*100/400 = 30%.

1) Gini coefficient is defined as a ratio of the area between the Lorenz curve of the distribution and the uniform distribution line (line of perfect equality) and the total area under the uniform distribution line

Area of region under the Lorenz curve = area of 1^st triangle + cumulative areas of four different trapeziums.

= 0.5*(20%)*(10%) + 0.5*(10% + 25%)*(20%) + 0.5*(25% + 45%)*(20%) + 0.5*(45% + 70%)*(20%) +0.5*(70% + 100%)*(20%) = 0.40

Area between the line of perfect inequality and Lorenz curve = 0.5 – 0.40 = 0.10. Gini coefficient = 0.10/050 = 20%.

2) The figure is drawn below.