Home / Questions / Lorenz Curve Economists use Lorenz curves to illustrate the distribution of income in a co...
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 the
presents 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 indicates a country's ''income inequality.''
The table lists the percent of income y for selected percent 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''.
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