Anthony B. Atkinson's paper "On the Measurement of Inequality" addresses the conceptual and theoretical issues surrounding the measurement of income inequality. He argues that conventional measures such as the variance, coefficient of variation, and Gini coefficient often obscure the underlying social welfare function and may not align with widely accepted principles of inequality aversion. Atkinson proposes a new approach based on a social welfare function that is symmetric and additively separable in individual incomes. This approach allows for a more direct comparison of distributions without the need to specify the form of the social welfare function explicitly. He introduces the concept of the equally distributed equivalent income (EDE) and defines a measure of inequality \( I \) as \( 1 - \frac{y_{\text{EDE}}}{\mu} \), where \( y_{\text{EDE}} \) is the level of income per head that would give the same level of social welfare if equally distributed. This measure is invariant under linear transformations of the social welfare function and provides a more intuitive way to compare distributions. Atkinson also discusses the properties of different measures, such as their sensitivity to transfers at different income levels, and concludes that the conventional measures often give conflicting rankings and may not reflect social values. He suggests that the new approach, based on the equally distributed equivalent measure, can provide a more consistent and interpretable way to measure inequality.Anthony B. Atkinson's paper "On the Measurement of Inequality" addresses the conceptual and theoretical issues surrounding the measurement of income inequality. He argues that conventional measures such as the variance, coefficient of variation, and Gini coefficient often obscure the underlying social welfare function and may not align with widely accepted principles of inequality aversion. Atkinson proposes a new approach based on a social welfare function that is symmetric and additively separable in individual incomes. This approach allows for a more direct comparison of distributions without the need to specify the form of the social welfare function explicitly. He introduces the concept of the equally distributed equivalent income (EDE) and defines a measure of inequality \( I \) as \( 1 - \frac{y_{\text{EDE}}}{\mu} \), where \( y_{\text{EDE}} \) is the level of income per head that would give the same level of social welfare if equally distributed. This measure is invariant under linear transformations of the social welfare function and provides a more intuitive way to compare distributions. Atkinson also discusses the properties of different measures, such as their sensitivity to transfers at different income levels, and concludes that the conventional measures often give conflicting rankings and may not reflect social values. He suggests that the new approach, based on the equally distributed equivalent measure, can provide a more consistent and interpretable way to measure inequality.