1 Suppose there are two countries with 10 people each Countr

1. Suppose there are two countries with 10 people each. Country A has an earnings distribution given by that in column 2 and Country B has an earnings distribution given by that in column 3. Which country has greater income inequality? a) For each country, calculate the following: variance ii coefficient of variation i the 80-20 ratio iv the 90-10 ratio b) Analyze your results. Which country has greater earnings inequality? Citizens Country A\'s Earnings Country B\'s Earnings 10 10 10 10

Solution

a)

i. Var for A=((1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(1-1.9)^2+(10-1.9)^2)/10 = 7.29

var for B = ((1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(10-2.8)^2+(10-2.8)^2)/10 = 12.96

ii. Coefficient of variation for A= (SD/mean)*100= (sqrt of var/mean)*100 = sqrt(7.29)/1.9 = 2.7/1.9 = 1.42

Coefficient of variation for B= (SD/mean)*100= (sqrt of var/mean)*100 = sqrt(12.96)/2.8 = 3.6/2.8 = 1.28

iii.the 80:20 ratio

for country A

80 percent of population earn 42.11 percent of income and 20 percent earn 57.89 percent of income

for country B

80 percent of population earn 28.57 percent of income and 20 percent earn 71.43 percent of income

iv the 90:20 ratio

for country A

90 percent of population earn 47.37 percent of income and 10 percent earn 52.63 percent of income

for country B

90 percent of population earn 64.29 percent of income and 10 percent earn 35.71 percent of income

b. Looking at the results, country A has more income inequality than country B

Citizens

A

B

Proportion of population (%)

Cumulative Proportion of population (%)

Income % of A

Cumulative Income % of A

Income % of B

Cumulative Income % of B

1

1

1

10.00%

10.00%

5.26%

5.26%

3.57%

3.57%

2

1

1

10.00%

20.00%

5.26%

10.53%

3.57%

7.14%

3

1

1

10.00%

30.00%

5.26%

15.79%

3.57%

10.71%

4

1

1

10.00%

40.00%

5.26%

21.05%

3.57%

14.29%

5

1

1

10.00%

50.00%

5.26%

26.32%

3.57%

17.86%

6

1

1

10.00%

60.00%

5.26%

31.58%

3.57%

21.43%

7

1

1

10.00%

70.00%

5.26%

36.84%

3.57%

25.00%

8

1

1

10.00%

80.00%

5.26%

42.11%

3.57%

28.57%

9

1

10

10.00%

90.00%

5.26%

47.37%

35.71%

64.29%

10

10

10

10.00%

100.00%

52.63%

100.00%

35.71%

100.00%

Citizens	A	B	Proportion of population (%)	Cumulative Proportion of population (%)	Income % of A	Cumulative Income % of A	Income % of B	Cumulative Income % of B
1	1	1	10.00%	10.00%	5.26%	5.26%	3.57%	3.57%
2	1	1	10.00%	20.00%	5.26%	10.53%	3.57%	7.14%
3	1	1	10.00%	30.00%	5.26%	15.79%	3.57%	10.71%
4	1	1	10.00%	40.00%	5.26%	21.05%	3.57%	14.29%
5	1	1	10.00%	50.00%	5.26%	26.32%	3.57%	17.86%
6	1	1	10.00%	60.00%	5.26%	31.58%	3.57%	21.43%
7	1	1	10.00%	70.00%	5.26%	36.84%	3.57%	25.00%
8	1	1	10.00%	80.00%	5.26%	42.11%	3.57%	28.57%
9	1	10	10.00%	90.00%	5.26%	47.37%	35.71%	64.29%
10	10	10	10.00%	100.00%	52.63%	100.00%	35.71%	100.00%