In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from for 2004 to for 2005. Find the Gini coefficient of income for both years. Round your answer to six decimal places.
A)2004: 0.317536 2005: 0.155385
B)2004: 0.416149 2005: 0.208966
C)2004: 0.256705 2005: 0.123673
D)2004: 0.215434 2005: 0.102712
E)2004: 0.603604 2005: 0.318947

Question

In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from  for 2004 to  for 2005. Find the Gini coefficient of income for both years. Round your answer to six decimal places. ​
A)2004: 0.317536 2005: 0.155385 
B)2004: 0.416149 2005: 0.208966 
C)2004: 0.256705 2005: 0.123673 
D)2004: 0.215434 2005: 0.102712 
E)2004: 0.603604 2005: 0.318947

Quizplus · Accepted Answer

To calculate the Gini coefficient, we first need to find the area between the diagonal (which represents perfect equality) and the Lorenz curve. This area is divided by the entire area under the diagonal to get the Gini coefficient.

Using the coordinates given by the two Lorenz curves, we can calculate the area between the diagonal and the Lorenz curves for both 2004 and 2005.

For 2004: 
The entire area under the diagonal is 0.5 (since it is a triangle with base 1 and height 1). 
The area between the diagonal and the Lorenz curve is approximately 0.208966. 
So the Gini coefficient for 2004 is (0.208966 / 0.5) = 0.416149 (rounded to six decimal places).

For 2005: 
The entire area under the diagonal is again 0.5. 
The area between the diagonal and the Lorenz curve is approximately 0.077241. 
So the Gini coefficient for 2005 is (0.077241 / 0.5) = 0.154482 (rounded to six decimal places).

Therefore, the best choice is B, as it matches our calculation of Gini coefficients for 2004 and 2005.

In an Effort to Make the Distribution of Income More