A country's Lorentz curve, y = L(x), provides us with insight into the country's income inequality. In particular, if the point (0; T00) is on the Lorentz curve, then this means that the bottom a% of households receive b% of the country's total income. In this context, the line y = x is called the perfect equality line (do you see why?). The Gini index of a country is defined to be the area of the region between the line y = x and the country's Lorentz curve y = L(x) on the interval 0, 1], and can be used to measure the income inequality of the country. Suppose there are two hypothetical countries A and B with Lorentz curves: LA(x) = x³, LB(x) = sin -x cos -x 2 (a) We can see that the point (0.5, 0.125) is on country A's Lorentz curve y = LA(x). From this, what can we conclude about the income distribution of the country A? (b) Compute the Gini indices of the countries A and B. Round your answers to the nearest 10th.

A country's Lorentz curve, y = L(x), provides us with insight into the country's income inequality. In particular, if the point (0; T00) is on the Lorentz curve, then this means that the bottom a% of households receive b% of the country's total income. In this context, the line y = x is called the perfect equality line (do you see why?). The Gini index of a country is defined to be the area of the region between the line y = x and the country's Lorentz curve y = L(x) on the interval 0, 1], and can be used to measure the income inequality of the country. Suppose there are two hypothetical countries A and B with Lorentz curves: LA(x) = x³, LB(x) = sin -x cos -x 2 (a) We can see that the point (0.5, 0.125) is on country A's Lorentz curve y = LA(x). From this, what can we conclude about the income distribution of the country A? (b) Compute the Gini indices of the countries A and B. Round your answers to the nearest 10th.

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter20: Poverty, Inequality, And Discrimination

Section: Chapter Questions

Problem 5DQ

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