Chapter 6.1, Problem 90E

Income distribution. Using data from the U.S. Census Bureau, an economist produced the following Lorenz curves for the distribution of U.S. income in 1962 and in 1972:

     $\begin{array}{cc}f\left(x\right)=\frac{3}{10}x+\frac{7}{10}{x}^2& \text{Lorenz}\text{curve}\text{for}1962\\ g\left(x\right)=\frac{1}{2}x+\frac{1}{2}{x}^2& \text{Lorenz}\text{curve}\text{for}1972\end{array}$

Find the Gini index of income concentration for each Lorenz curve and interpret the results.