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This paper explores, in the context of the Atkinson inequality measure, attempts to make interpretations of orders of magnitude transparent. One suggestion is that the analogy of sharing a cake among a very small number of people provides a useful intuitive description for people who want some idea of what an inequality measure 'actually means'. In contrast with the Gini measure, for which a simple 'cake-sharing' result is available, the Atkinson measure requires a nonlinear equation to be solved. Comparisons of 'excess shares' (the share obtained by the richer person in excess of the arithmetic mean) for a range of assumptions are provided. The implications for the 'leaky bucket' experiments are also examined. An additional approach is to obtain the 'pivotal income', above which a small increase for any individual increases inequality. The properties of this measure for the Atkinson index are also explored.
I have benefited from detailed comments by Anita King and Justin van de Ven on an earlier draft. I am grateful to Nicolas Hérault and Stephen Jenkins for drawing my attention to literature on the pivotal income.
The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government. The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate.
Table of Contents
- Executive Summary
- 1 Introduction
- 2 Previous Results for the Gini Measure
- 3 The Atkinson Inequality Measure
- 4 The Abbreviated Welfare Function
- 5 An Equivalent Small Distribution
- 6 The Pivotal Income
- 7 Conclusions
- Appendix A: The Gini Inequality Measure