QuestionUsing data from a nation's census, an economist produced the following Lorenz curves for the distribution of that nation's income in 1962 and 1972. $$\begin{array}{ll} f(x)=\frac{1}{2} x+\frac{1}{2} x^{2} & \text { Lorenz curve for } 1962 \\ g(x)=\frac{2}{5} x+\frac{3}{5} x^{2} & \text { Lorenz curve for } 1972 \end{array}$$
Find the Gini index of income concentration for each Lorenz curve and interpret the results.
Identify the integrand for the computation of the Gini index for 1962 and 1972.
The Gini index for 1962 is given by $2 \int_{0}^{1}\left(\square d^{2} x\right.$ and the Gini index for 1972 is given by $2 \int_{0}^{1} \square d x$.