Chapter 7.1, Problem 77E

Lorenz Curve Economists use Lorenz curves to illustrate the distribution of income in a country. A Lorenz curve, $y=f(x)$, represents the actual income distribution in the country. In this model, x represents percents of families in the country from the poorest to the wealthiest and y represents percents of total income The model $y=x$ represents a country in which each family has the same income. The area between these two models, where $0\le x\le 100$ indicates a country’s “income inequality." The table lists percents of income y for selected percents of families x in a country.

x	10	20	30	40	50
y	3.35	607	9.17	13.39	19.45

x	60	70	80	90
y	28.03	39.77	55.28	75.12

(a) Use a graphing utility to find a quadratic model for the Lorenz curve.

(b) Plot the data and graph the model.

(c) Graph the model $y=x$. How does this model compare with the model in part (a)?

(d) Use the integration capabilities of a graphing utility to approximate the “income inequality."