Question

a. What is the value of the Gini coefficient if area B is twice as large as area A?

b. Suppose that the Lorenz curve becomes more bowed, with the result that area B becomes exactly the same size as area A. What will be the new value of the Gini coefficient?

Short answer

a.$33.33\%$

b.$50\%$

Step-by-step solution

Given Information

The Gini coefficient is the proportion of the region between the line of amazing equity and the line of wonderful inequality. Greater inequality implies higher coefficient as well as the other way around.

Explanation Part (a)

a. We know,$\text{Gini Coefficientis}A/(A+B)$

Area B = 2 Area A

Hence the Gini coefficient is $A/(A+B)=A/3A=1/3$

which is $33.33\%$

Explanation Part (b)

b. We know,

Area B = Area A

Hence, the Gini coefficient is $A/(A+B)=A/2A=1/2$

which is$50\%$