Question

Analyze this distribution of income. Draw the Lorenz curve. Complete the Gini index. Calculate top income shares. Income groups Group members Group income 350 2,500 250 5,000 150 15,000 60,000 50 Sum

Answer 1

income group	group members	population composition %	group income	income composition %
1	350	43.75	2500	3.03
2	250	31.25	5000	6.06
3	150	18.75	15000	18.18
4	50	6.25	60000	72.72
sum	800	100	82500	100

% of theoret 27.27 9.097 3.037 43.75 75 9375 % of population Scanned with CamScanner

The distribution of income is highly unequal. More than 90% of the population lives with less than 30% of the total income.

The lorenz curve is as shown in the diagram with cumulative percentage of population on X axis and cumulative percentage of income on the Y axis.

Coordinates are

A (43.75,3.03) ; B (75,9.09) ; C(93.75, 27.27)

Gini Index Calculation

Formula:
G = 1/2n?uΣΣη;nuly; - Jel)
where
lhi' u u/=n

The top income shares are held by income group 4. It accounts for 72.73% of the total income.

M = I Enjy; I sr (350)(2500) +(250)(5000) + L (150) (15000) + 50 (60000) = 9218.75 M3 Ikle 1 k- 2 (A2) u fl k=1 Tk II j 1 % (350x250)| 2500 – 5000| +(250x150) | 1000-11000l+ 2(0)+(9218.75%(ISON SO) 15000-60000| +(350x 150) |2500 – 15000| + (350x50)|2-0060000 tesoxso)|5000-600cd 3500,000,000 2 * 1640,000) (9218.75-) 0.2966

The gini index calculated is 0.2966