# **6.4 Simulation Results**

We present optimal tax schedules using the distributions of productivities and preferences from Section 5 that correspond to (1) the baseline labor supply elasticity estimates from Chetty (2012) ( _ξz_<sup>_c_=</sup><sup>_ξ_</sup> _h_<sup>_c_=</sup><sup>_ξ_</sup> _z_<sup>_u_=</sup><sup>_ξ_</sup> _h_<sup>_u_=0</sup><sup>_._15),(2)alargereffortelasticity(</sup><sup>_ξ_</sup> _z_<sup>_c_=</sup><sup>_ξ_</sup> _z_<sup>_u_=</sup> 0 _._ 15 _, ξh_<sup>_c_=</sup><sup>_ξ_</sup> _h_<sup>_u_= 0</sup><sup>_._05),and(3)largerincomeeffects(</sup><sup>_ξ_</sup> _z_<sup>_c_=</sup><sup>_ξ_</sup> _h_<sup>_c_= 0</sup><sup>_._15</sup><sup>_, ξ_</sup> _z_<sup>_u_=</sup><sup>_ξ_</sup> _h_<sup>_u_= 0).Along</sup> with each optimal tax schedule we plot the Mirrleesian optimal schedule that assumes all income inequality is due to productivity differences. The optimal tax schedules corresponding to the baseline case, larger effort elasticity case, and larger income effects are shown in Figures 10a, 10b, and 10c, respectively. We choose to plot _average_ tax rates (as opposed to marginal tax rates, which can be found in Figure 23 in the Appendix) as this conveys the tax burden at each income level under the different distributions of productivities and preferences implied by the different values of the labor supply elasticities.<sup>36</sup> Note that different elasticity estimates imply different efficiency costs of taxation (so that the Mirrleesian benchmark is not constant across all the different elasticity estimates). The important aspect to focus on then is the _difference_ in tax rates between the Mirrleesian benchmark and our optimal tax schedules that account for both productivity and preference heterogeneity driving income inequality; this difference in tax rates is not driven by differences in the efficiency costs of taxation but by differences in the equity of taxation.

In Figure 10a, optimal average tax rates computed assuming both _n_ and _α_ heterogeneity are relatively similar to, but (almost) everywhere _≈_ 2 p.p. _higher_ than, the benchmark Mirrleesian rates, which assume all income inequality is driven by _n_ heterogeneity. This is because, under our baseline elasticity estimates, productivity heterogeneity drives most of income inequality and high income individuals have lower preferences on average, so that redistributing away from them is slightly more desirable than in the Mirrleesian benchmark. On the other hand, in Figures 10b and 10c (which correspond to a higher effort elasticity and larger income effects, respectively) we find that average tax rates are now lower than the Mirrleesian benchmark. Higher effort elasticities and larger income effects both lead to lower optimal tax rates relative to the Mirrleesian optimal tax schedule. This is because higher effort elasticities and larger income effects both imply that high income individuals have higher preferences for consumption, so that redistributing away from them is less desirable than in the Mirrleesian benchmark.

> 36Note, all individuals receive a lump-sum transfer under every optimal schedule. This transfer is increasing with overall tax rates and is excluded from income when calculating average tax rates.

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