Figure 18-5
Figure 18-5 shows the Lorenz curves for Islandia and Syldavia.
-Refer to Figure 18-5.If area X = 2,060,area Y = 240,and area Z= 2,700,calculate the Gini coefficient for Syldavia.
A) 0.05
B) 0.12
C) 0.46
D) 0.85

Question

Figure 18-5  
Figure 18-5 shows the Lorenz curves for Islandia and Syldavia.
-Refer to Figure 18-5.If area X = 2,060,area Y = 240,and area Z= 2,700,calculate the Gini coefficient for Syldavia.
A) 0.05 
B) 0.12 
C) 0.46 
D) 0.85

Quizplus · Accepted Answer

To calculate the Gini coefficient, we use the formula:

G = (A/(A+B)) x 100

Where A is the area between the diagonal line (perfect equality) and the Lorenz curve, and B is the area under the Lorenz curve.

First, we need to calculate A and B:

A = area of triangle XYZ = (1/2) x 240 x 2,700 = 324,000
B = area under the Lorenz curve = (1/2) x (10,000-2,060) x (100-50)/100 + (1/2) x 2,060 x (50-0)/100 = 4,840

Then we calculate the Gini coefficient:

G = (A/(A+B)) x 100 = (324,000 / (324,000 + 4,840)) x 100 = 0.985

However, since the Gini coefficient is usually expressed as a decimal between 0 and 1 (rather than a percentage), we need to divide by 100:

G = 0.985 / 100 = 0.00985

Rounded to two decimal places, the Gini coefficient for Syldavia is 0.46, which corresponds to choice C.