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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 rep

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''.

 

 

Jun 24 2021 View more View Less

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