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A note on the relationship between additive separability and decomposability in measuring income inequality

Fine, Ben; Mendes Loureiro, Pedro

Authors

Pedro Mendes Loureiro



Abstract

This note introduces original technical results in the theoretical measurement of inequality by specifying the relationships between additive separability and homotheticity (of measures of welfare closely related to measures of inequality), and decomposability and homogeneity in measures of inequality. More specifically, an interrogation is made of the resonances and dissonances between the classic contributions of Atkinson and Shorrocks, which are key representatives, respectively, of the 'social welfare function' and the 'axiomatic' approaches to measuring inequality. In brief, in the presence of otherwise common assumptions, it is shown that additive separability and homotheticity of welfare are stronger combined conditions than decomposability and homogeneity (of degree zero) of income inequality. The gap between the two, however, can be closed by adding an extra term around total income to the measure of welfare, allowing for wider considerations of the relationship between social welfare, total income, and the distribution of individual incomes.

Citation

Fine, B., & Mendes Loureiro, P. (2022). A note on the relationship between additive separability and decomposability in measuring income inequality. Review of Social Economy, 80(4), 550-565. https://doi.org/10.1080/00346764.2020.1802055

Journal Article Type Article
Acceptance Date Jul 8, 2020
Online Publication Date Aug 6, 2020
Publication Date Nov 1, 2022
Deposit Date Aug 11, 2020
Journal Review of Social Economy
Print ISSN 0034-6764
Electronic ISSN 1470-1162
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 80
Issue 4
Pages 550-565
DOI https://doi.org/10.1080/00346764.2020.1802055
Publisher URL https://www.tandfonline.com/doi/abs/10.1080/00346764.2020.1802055
Related Public URLs https://www.soas.ac.uk/economics/research/workingpapers/file141391.pdf


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