Atkinson index: Difference between revisions

Revision as of 04:01, 11 October 2015

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==Definition==

The index can be turned into a [[Normative economics|normative]] measure by imposing a [[coefficient]] <math>\varepsilon</math> to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing <math>\varepsilon</math>, the level of "inequality aversion", appropriately. The Atkinson index becomes more sensitive to changes at the lower end of the income distribution as <math>\varepsilon</math> approaches 1. Conversely, as the level of inequality aversion falls (that is, as <math>\varepsilon</math> approaches 0) the Atkinson becomes lessmore sensitive to changes in the lowerupper end of the income distribution.

The Atkinson <math>\varepsilon</math> parameter is often called the "inequality aversion parameter", since it quantifies the amount of social utility that is assumed to be gained from complete redistribution of resources. For <math>\varepsilon=0</math>, (no aversion to inequality) it is assumed that no social utility is gained by complete redistribution and the Atkinson index (<math>A_\varepsilon</math>) is zero. For <math>\varepsilon=\infty</math> (infinite aversion to inequality), it is assumed that infinite social utility is gained by complete redistribution in which case <math>A_\varepsilon=1</math>. The Atkinson index (<math>A_\varepsilon</math>) then varies between 0 and 1 and is a measure of the amount of social utility to be gained by complete redistribution of a given income distribution. Based on one's value judgement concerning the social utility of complete redistribution, as embodied in the <math>\varepsilon</math> parameter, different income distributions may be compared by calculating the Atkinson index at that <math>\varepsilon</math> value, with lower values of <math>A_\varepsilon</math> indicating lower social utility to be gained, higher values indicating more. Lower values of <math>A_\varepsilon</math> thus indicate a more equal distribution than higher values, given a particular degree of inequality aversion.