Question

1. The function L(x)=0.6847x^2+0.0522x represents the Lorenz Curve for Country Y’s income distribution in 1996.

   a Compute the percent of wealth the upper 30% of the population controlled. bCompute the percent of wealth the lower 60% of the population controlled. c Determine the Gini index of Country Y.

Answer 1

LORENZ CURVE shows the cumulative population on x axis and cumulative income on y axis.

Given function is L(x)=0.6847 x² + 0.0522x

For the entire population i.e. x=1 the wealth held by the society is

L(1)= 0.6847*1+0.0522= 0.7369

For the lower 70% x=0.7 , thus wealth held by lower 70% is

L(0.7)= 0.6847*0.7*0.7+0.0522*0.7=0.3720

Thus wealth held by upper 30% of population is 0.7369-0.3720=0.3649

Percentage of wealth held by upper 30%= 0.3649/0.7369*100=49.5 or 50%

For the lower 60% of the population x=.6

L(0.6)=0.6847*0.6*0.6+0.0522*0.6=0.2778

Percentage of wealth held= 0.2778/0.7369*100=37.69 or 38%