Chapter 6.1, Problem 92E

Learning. Repeat Problem 91 if $V\prime \left(t\right)=13/t^{1/2}$ and the interval is changed to [1, 4].

91. Distribution of wealth. Lorenz curves also can provide a relative measure of the distribution of a country’s total assets. Using data in a report by the U.S. Congressional Joint Economic Committee, an economist produced the following Lorenz curves for the distribution of total U.S. assets in 1963 and in 1983:

     $\begin{array}{l}f\left(x\right)=x^{10} \text{Lorenz curve for }1963\hfill \\ g\left(x\right)= x^{12} \text{Lorenz curve for }1983\hfill \end{array}$

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