Question

An economist seeks to measure the degree of income inequality in a society. Assume that there are a large number of individuals in the society. Three quarters of the individuals have an income of 10, and one quarter of the individuals have an income of 30. What is the Gini coefficient in this example? (Graphically)

Answer 1

Total income is 40. Three quarters of the individuals or 75% of population is earning 10 or 25% of income and remaining 25% of population is earning remaining 30 or 75% of income. Hence we draw the Lorenz curve below that has a kink at 75% of population and 25% of income

Cumulative % of income Line of perfect equality Lorenz curve lo 25 50 75 100 Cumulative % of population

First find the Area of region under the Lorenz curve = 0.5*(75% - 0%)*25% + 0.5*(100% + 25%)*25%

= 0.25

Area between the line of perfect inequality and Lorenz curve = 0.5 – 0.25 = 0.25

Gini coefficient = 0.25/0.50 = 0.50

Cumulative,% of income Gini coefficient = A (A+B) 50 75 100 Cumulative % of population