Separated into 6 questions to make it worth your time 4 Whic

Separated into 6 questions to make it worth your time:

4) Which nation experiences the lowest level of income inequality?

Suppose you\'re an economist working for the Brookings Institute and you\'ve been asked to comment on what you see as a diverging level of inequality among representative households in two neighboring nations: Mira and Drovanna. You have the following information about these nations\' households for 2014 (income values in 2014 US dollar equivalencies) Mira Drovanna 16000 28000 11000 32000 900056000 18000 43000 15000 88000 126000 36000 22000 27000 31000 61000 10000 59000 12000 48000 The Brookings Institute is about to recommend one of these nations to the World Bank as a nation deserving of additional development funds due to its significant need to close its income gap, the other will be recognized for its relatively low level of income inequality.

Solution

The income inequality in each country can be calculated with the help of Gini Coefficient from the given data.

Mira ($)

Drovanna ($)

9000

27000

10000

28000

11000

32000

12000

36000

15000

43000

16000

48000

18000

56000

22000

59000

31000

61000

126000

88000

Quintile

Income of Mira ($)

Percentage of Mira’s income (%)

Cumulative % of Mira’s income (%)

Cumulative proportion of Mira’s income

Income of Drovanna ($)

Percentage of Drovanna’s income

Cumulative % of Drovanna’s income

Cumulative proportion of Drovanna’’s income

20

19000

7.04

7.04

70.4/100 = 0.07

55000

11.51

11.51

0.12

40

23000

8.52

15.56

0.16

68000

14.23

25.73

0.26

60

31000

11.48

27.04

0.27

91000

19.04

44.77

0.45

80

40000

14.81

41.85

0.42

115000

24.06

68.83

0.69

100

157000

58.15

100.00

1.00

149000

31.17

100.00

1.00

Total

270000

100.00

478000

100.00

If we find out the area lying below each country’s Lorenz curve, and subtract it from the area of the right angled triangle (0.5), then we can get the area lying within each country’s Lorenz curve. The Gini Coefficient for each country would then be the ratio of the area lying within each country’s Lorenz curve to the area of the triangle (0.5).

The calculations have been done in the table below.

It is important to note that for calculating the area below the Lorenz curve, if the whole curve is divided into rectangles, then the area of each rectangle equals the sum of its previous cumulative % of income and its own cumulative percentage of income, whole divided by 2, times the width of each rectangle. All these individual areas are summed to get the area under the Lorenz curve for each country.

Quintile

Cumulative proportion of Mira’s income

Area under the Lorenz Curve of Mira

Cumulative proportion of Drovanna’’s income

Area under the Lorenz Curve of Drovanna

0

0

0

0

0

20

0.07

[(0.07+0)/2]*0.10 = 0.0035

0.12

[(0.12+0)/2]*0.10

=

0.0058

40

0.16

0.0113

0.26

0.0186

60

0.27

0.0213

0.45

0.0353

80

0.42

0.0344

0.69

0.0568

100

1.00

0.0709

1.00

0.0844

Total

0.1415

0.2008

Since there are 5 observations here, there are 5 rectangles and the width of each rectangle is 5 = 0.20.

The Gini Coefficient of Mira is therefore 0.5-0.1415= 0.3585

The Gini Coefficient of Drovanna is therefore 0.5-0.2008 = 0. 0.2992

Since a Gini coefficient of 1 denotes perfect inequality, Mira is has higher inequality than Drovanna.

Therefore the lowest level of income inequality is experienced by nation Drovanna.

Mira ($)	Drovanna ($)
9000	27000
10000	28000
11000	32000
12000	36000
15000	43000
16000	48000
18000	56000
22000	59000
31000	61000
126000	88000