Question

Consider the following two earnings distributions for two countries (Country A and Country B).

a) Calculate the following for each country:

i) the variance of earnings

ii) the coefficient of variation for earnings

iii) the 80-20 ratio

iv) the area under the Lorenz Curve for earnings

v) the Gini Coefficient for earnings.

b) Comparing your answers in part a, which country has greater earnings inequality?

Country A			Country B
Worker	Earnings	Worker		Earnings
1	1	1		1
2	1	2		10
3	1	3		10
4	1	4		10
5	10	5		10

Answer 1

country A

mean = (1+1+1+1+10)/5 = 14/5 =2.8

var = ((1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(1-2.8)^2+(10-2.8)^2)5 = 16.2

coefficient =var/sd = 12.96/2.8 =5.8

80-20 1:10

4)

c population	c income	% pop	%inc
1	1	20%	7%
2	2	40%	14%
3	3	60%	21%
4	4	80%	29%
5	14	100%	100%

=.5*(.07+.76)*.60 +.5*(.76+1.00)*.20

.425

5)

= .51

for country B similarly

country A

mean = (1+1+10+10+10)/5 = 8.2

var = 16.2

coefficient =var/sd = 16.2/8.2=1.97

80-20 10:1

4)

cupopulation	c income	% pop	%inc
1	1	20%	2%
2	11	40%	27%
3	21	60%	51%
4	31	80%	76%
5	41	100%	100%

area = .5(.02+1)*.80 =.40

5)

= .175

b)

clearly there is more inequality in country A