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The Pareto-Frontier in a Simple Mirrleesian Model of Income Taxation

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Abstract

We characterize the Pareto-frontier in a simple Mirrleesian model of income taxation. We show how the second-best frontier which incorporates incentive constraints due to private information on productive abilities relates to the first-best frontier which takes only resource constraints into account. In particular, we argue that the second-best frontier can be interpreted as a Laer-curve. We also use this second-best frontier for a comparative statics analysis of how optimal income tax rates vary with the degree of inequity aversion, and for a characterization of optimal public-good provision. We show that a more inequity averse policy maker chooses tax schedules that are more redistributive and involve higher marginal tax rates, but chooses a lower public-goods provision level.

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... The general intuition is that more redistribution from high-skilled individuals to low-skilled individuals goes together with more distortionary taxation. The validity of this intuition is formally confirmed in Bierbrauer and Boyer (2010) who show that the marginal tax rates of low-skilled and high-skilled individuals, respectively, are non-decreasing functions of v L. 21 ...
... is the Pareto-frontier in a simplified version of the Mirrleesian optimal income tax problem that does not contain a decision on public-goods provision. The properties of this Pareto-frontier are extensively studied in Bierbrauer and Boyer (2010). The derivations that follow make repeated use of these properties. ...
... Since it is linear in u1, and u2, this follows from the fact that VH is a concave function of vL and r(q). A proof of this assertion can be found in Bierbrauer and Boyer (2010). and ...
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We study how an optimal income tax and an optimal public-goods provision rule respond to preference and productivity shocks. A conventional Mirrleesian treatment is shown to provoke manipulations of the policy mechanism by individuals with similar interests. We therefore extend the Mirrleesian model so as to include a requirement of coalition-proofness. The main results are the following: first, the possibility of preference shocks yields a new set of collective incentive constraints. Productivity shocks have no such implication. Second, the optimal policy gives rise to a positive correlation between the public-goods provision level, the extent of redistribution and marginal tax rates.
... All proofs are in the Appendix. The formal analysis repeatedly refers to results that can be found in Bierbrauer and Boyer (2010), a note which contains, for a simple model of non-linear income taxation, a complete analytical characterization of all Pareto-efficient tax schedules. ...
... (1) 8 For the given environment, Bierbrauer and Boyer (2010) provide a complete analytical characterization of the set of Pareto-efficient income tax schedules. It follows from their analysis -particularly, from arguments in the proof of Proposition 1 -that non-negativity constraints on consumption levels can be safely ignored, for every Pareto-efficient income tax schedule, if ω L ω H ≥ f H . ...
... However, the logic of the analysis would remain the same with alternative assumptions about the mechanism designer's beliefs. 29 For a complete characterization of the function V H , see Proposition 1 in Bierbrauer and Boyer (2010). ...
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We study optimal income taxation and public-goods provision under the as-sumption that the cross-section distributions of productive abilities or public-goods preferences are not known a priori. A conventional Mirrleesian treatment is shown to provoke manipulations of the policy mechanism by individuals with similar inter-ests. The analysis therefore incorporates a requirement of coalition-proofness. The main result is that increased public-goods provision is associated with a more dis-tortionary and a more redistributive tax system. With a conventional Mirrleesian treatment, the level of public-goods provision is not related to how distortionary or redistributive the tax system is.
... The numerical values on the horizontal axis are therefore different from those on the vertical axis. A complete analytical characterization can be found in Bierbrauer and Boyer (2010). ...
... 12 A proof of the Proposition can be found in Bierbrauer and Boyer (2010). ...
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