Chapter 6.1, Problem 92E

Income distribution. The government of a small country is planning sweeping changes in the tax structure in order to provide a more equitable distribution of income. The Lorenz curves for the current income distribution and for the projected income distribution after enactment of the tax changes are as follows:

     $\begin{array}{l}f\left(x\right)=x^{2.3}\text{Current Lorenz curve}\hfill \\ g\left(x\right)=0.4x+0.6x^2\text{Projected Lorenz curve after changes in tax laws}\hfill \end{array}$

Find the Gini index of income concentration for each Lorenz curve. Will the proposed changes provide a more equitable income distribution? Explain.