### Abstract

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.

Original language | English |
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Pages (from-to) | 99-123 |

Number of pages | 25 |

Journal | Economic Theory |

Volume | 65 |

Issue number | 1 |

Early online date | 2 Nov 2016 |

DOIs | |

Publication status | Published - Jan 2018 |

### Keywords

- measurement of inequality
- discrete data
- majorization set
- majorization matrix
- convex sets and their separation

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## Cite this

Abul Naga, R. H. (2018). Measurement of inequality with a finite number of pay states: the majorization set and its applications.

*Economic Theory*,*65*(1), 99-123. https://doi.org/10.1007/s00199-016-1011-2