Bunching in rank-dependent optimal income tax schedules

Laurent Simula and Alain Trannoy

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Abstract: Considering optimal non-linear income tax problems when the social welfare function only depends on ranks as in Yaari (Econometrica 55(1):95–115, 1987) and weights agreeing with the Lorenz quasi-ordering, we extend the analysis of Simula and Trannoy (Am Econ J Econ Policy, 2021) in two directions. First, we establish conditions under which bunching does not occur in the social optimum. We find a sufficient condition on individual preferences, which appears as a reinforcement of the Spence-Mirrlees condition. In particular, the marginal dis-utility of gross income should be convex, but less convex the higher the productivity. We also show that, for all productivity distributions with a log-concave survival function, bunching is precluded under the maximin, Gini, and "illfare-ranked single-series Ginis". Second, we turn to a discrete population setting, and provide an "ABC" formula for optimal marginal tax rates, which is related to those for a continuum of types found in Simula and Trannoy (2021), but remain essentially distinct.

Keywords: Rank dependence; Gini; Optimal Income Taxation; Bunching; Log-Concavity (search for similar items in EconPapers)
Date: 2023-01
New Economics Papers: this item is included in nep-pub and nep-upt
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Published in Social Choice and Welfare, 2023, 60 (1), pp.237-263. ⟨10.1007/s00355-021-01384-1⟩

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Journal Article: Bunching in rank-dependent optimal income tax schedules (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03550894

DOI: 10.1007/s00355-021-01384-1

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