### Abstract

Original language | English |
---|---|

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 |

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### Keywords

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

### Cite this

*Economic Theory*,

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

**Measurement of inequality with a finite number of pay states : the majorization set and its applications.** / Abul Naga, Ramses H. (Corresponding Author).

Research output: Contribution to journal › Article

*Economic Theory*, vol. 65, no. 1, pp. 99-123. https://doi.org/10.1007/s00199-016-1011-2

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TY - JOUR

T1 - Measurement of inequality with a finite number of pay states

T2 - the majorization set and its applications

AU - Abul Naga, Ramses H.

N1 - I am grateful to Vassily Gorbanov, Tarik Yalcin and Fabrizio Germano for extended discussions and suggestions, and to an associate editor and a reviewer for constructive comments. I also wish to thank Francesco Andreoli, Geoffrey Burton, Joe Swierzbinski, Alain Trannoy, Claudio Zoli and seminar participants at the Aix-Marseille School of Economics for discussions. I am responsible for any errors.

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

KW - measurement of inequality

KW - discrete data

KW - majorization set

KW - majorization matrix

KW - convex sets and their separation

U2 - 10.1007/s00199-016-1011-2

DO - 10.1007/s00199-016-1011-2

M3 - Article

VL - 65

SP - 99

EP - 123

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

IS - 1

ER -