CPS-UIC Math Forum Gini Index

Integrals and Equity

http://www.rethinkingschools.org/archive/19_03/inte193.shtml

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Measuring inequality of distribution of income by the [Corrado] Gini Index

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Lorenz Curve: Graph of Cumulative Percentage vs. Cumulative Percentage

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Gini Index =¹ 100 × (Gini Coefficient)

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Simple Example: If the population is divided into two groups - the rich 20% and the poor 100 − 20 = 80% and the rich control 90% of the income, the Gini Index is g = 90 −20 = 70. See Fig.2 in http://www.cr1.dircon.co.uk/pdffiles/Lorenz.pdf Thus the Gini Index is the incremental advantage of the rich population.

Gini Coefficient

http://en.wikipedia.org/wiki/Gini_coefficient

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Advantages and Disadvantages of the Gini coefficient as a measure of inequality

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Advantages: Anonymity, Scale independence, Population independence

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Disadvantages: Units of Measurement, Households vs. Individuals, Definition of Income.

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Policy Considerations: FRBSF: Economic Letter - Inequality in the United States

http://www.frbsf.org/econrsrch/wklyltr/el97-03.html

Simple Example

Simple Example: If the population is divided into two groups - the rich proportion r and the poor proportion 1− r and the rich control an r + g proportion of the the total income, the Gini Coefficient is g = (r + g) − r. If there was complete equity , the rich would control r and g represents the incremental advantage of the rich.

In the figure, A = (1,1), q = GH = CD, and

Area ∆OCA = Area ∆OCD + Area ∆DCA = 1 2 CD ·OB + 1 2 BF ·OB = 1 2 CD ·OF = 1 2 q,

or

Area ∆OCA Area ∆OFA = q.

Footnotes: