Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on this curve are determined by ranking all households by income and then computing the percentage of households whose income is less than or equal to a given percentage of the total income of the country. For example, the point (a/100, b/100) is on the Lorenz curve if the bottom a% of the households receive less than or equal to b% of the total income. "Absolute equality" of income distribution would occur if the bottom a% of the households receive a% of the income, in which case the Lorenz curve would be the line y=x. The area between the Lorenz curve and the line y=x measures how much income distribution differs from absolute equality. The "coefficient of inequality" is the ratio of the area between the Lorenz curve and the line y=x to the area under y=x.

a) Show that the coefficient of inequality is twice the area between the Lorenz curve and the line y=x; that is, show that the coefficient of inequality = (2)the integral from 0 to 1 of [x-L(x)]dx.

b)The income distribution for a certain country is represented by the Lorenz curve defined by the equation L(x)=(5/12)x^2+(7/12)x. What is the percentage of total income received by the households? Find the coefficient of inequality.

Solution Summary

This is a problem regarding a Lorenz curve and the coefficients of inequality.

Lorenz Curve: Distribution of Wealth in the United States. ... The Lorenz curve is attached. It is the same curve that has been attached in Solution: 505472. ...

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... a) draw the lorenz curve for this case (This is the part I did). ... a) draw the lorenz curve for this case (This is the part I did). I dont understand part B: ...

... a. Gini coefficient is the area between the Line of equality and the Lorenz curve, divided by the total area of the half-square in which the curve lies. ...

... of this crop is best represented by a shift to the right in the supply curve. ... 9. All real-world Lorenz curves are above the 45-degree line because income is ...

... of this crop is best represented by a shift to the right in the supply curve. ... 9. All real-world Lorenz curves are above the 45-degree line because income is ...

... You can tell by the slopes of the Lorenz curves which economy is the most inequity. ... Brazil's Lorenz curve is farthest from the 45 degree line. ...