3. Working backwards: In 2011, the CIA website reported that the Gini index for the distribution of family income in the US was .45 . (a) Assume that the Lorenz curve for this distribution has the simple form f(x) = x^p. Determine the number p that matches the given value for the Gini. (b) According to this model, how much of the family income is earned by the top 5% of families?
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The Gini index is defined as the ratio of the area between the Lorenz curve and the line of perfect equality to the total area under the line of perfect equality. Mathematically, it can be expressed as: $$G = \frac{1}{2} - \int_0^1 f(z) dz$$ Show more…
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'The national income distribution in the United States in 2010 follows Lorenz curve y = L(x) which passes through these points: 0.2 0.4 0.6 0.8 0.051 0.156 0.313 0.542 Use the Trapezoid Rule to estimate the GINI Index for the United States in 2010. The national income distribution in the United States in 2016 follows Lorenz curve y = L(x) which passes through these points: 0.2 0.4 0.6 0.8 0.05 0.152 0.305 0.531 Use the Trapezoid Rule to estimate the GINI Index for the United States in 2016_ Compared with 2010, was the income distribution in the United States in 2016 more equal or less equal? more equal less equal'
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Income distribution. Find the Gini index of income concentration for the Lorenz curve with equation $$y=x e^{x-1}$$
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