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The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality.^{[1]}
The index can be turned into a normative measure by imposing a coefficient \varepsilon to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing \varepsilon, the level of "inequality aversion", appropriately. The Atkinson index becomes more sensitive to changes at the lower end of the income distribution as \varepsilon approaches 1. Conversely, as the level of inequality aversion falls (that is, as \varepsilon approaches 0) the Atkinson becomes more sensitive to changes in the upper end of the income distribution.
The Atkinson \varepsilon parameter is often called the "income aversion parameter", since it quantifies the amount of social utility that is assumed to be gained from complete redistribution of resources. For \varepsilon=0, (no aversion to inequality) it is assumed that no social utility is gained by complete redistribution and the Atkinson index (A_\varepsilon) is zero. For \varepsilon=\infty (infinite aversion to inequality), it is assumed that infinite social utility is gained by complete redistribution in which case A_\varepsilon=1. The Atkinson index (A_\varepsilon) 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 \varepsilon parameter, different income distributions may be compared by calculating the Atkinson index at that \varepsilon value, with lower values of A_\varepsilon indicating lower social utility to be gained, higher values indicating more. Lower values of A_\varepsilon thus indicate a more equal distribution than higher values, given a particular degree of inequality aversion.
The Atkinson index is defined as:
where y_{i} is individual income (i = 1, 2, ..., N) and \mu is the mean income.
Atkinson index relies on the following axioms:
where g indexes groups, i, individuals within groups, \mu_g is the mean income in group g, and the weights w_g depend on \mu_g, \mu, N and N_g. The class of the subgroup-decomposable inequality indices is very restrictive. Many popular indices, including Gini index, do not satisfy this property.
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Atlanta, United States Department of Commerce, Southern United States, New England, Philadelphia
Game theory, Microeconomics, Economics, Social choice theory, Pareto efficiency
Economics, Economic history, Mathematics, Computer science, Microeconomics
London School of Economics, Income distribution, University of Cambridge, Authority control, Nuffield College, Oxford