Measurement of inequality with a finite number of pay states: the majorization set and its applications

In this paper we examine the Lorenz ordering when the number of pay states is finite, as is most often the case in public sector employment. We characterize the majorization set: the set of pay scales such that some distribution u is more egalitarian than another distribution v, with u and v being t...

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Bibliographic Details
Published in:Economic theory 2018-01, Vol.65 (1), p.99-123
Main Author: Naga, Ramses H. Abul
Format: Article
Language:English
Subjects:
Economic models
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Egalitarianism
Employment
Equality
Game Theory
Inequality
Measurement
Microeconomics
Public Finance
Public sector
Research Article
Social and Behav. Sciences
Taxation
Wages and salaries
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Summary:In this paper we examine the Lorenz ordering when the number of pay states is finite, as is most often the case in public sector employment. We characterize the majorization set: the set of pay scales such that some distribution u is more egalitarian than another distribution v, with u and v being two distributions of a given sum total. We show that while this set is infinite, it is generated as the convex hull of a finite number of points. We then discuss several applications of the result, including the problem of reducing inequality between groups, conditions under which different pay scales may reverse the ordering of two Lorenz curves, and the use of the majorization set in relation to optimal income taxation.
ISSN:0938-2259
1432-0479
DOI:10.1007/s00199-016-1011-2