We derive a fully non-linear optimal income tax schedule in the presence of private insurance. We fill the gap in the literature by studying the optimal tax formula with a comprehensive structure of the private markets—including incomplete markets models—both theoretically and quantitatively. As in the standard taxation literature without private insurance, the optimal tax formula can still be expressed in terms of standard sufficient statistics. With private insurance, however, the formula involves additional terms that reflect how the private market interacts with public insurance. For example, the optimal tax formula should also consider asset distribution and pecuniary externalities as well as the welfare effects of borrowing constraints.

中文翻译：

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私人保险的最佳税收

在私人保险存在的情况下，我们得出了一个完全非线性的最优所得税表。我们通过在理论上和数量上研究具有私人市场综合结构（包括不完全市场模型）的最优税收公式来填补文献中的空白。正如在没有私人保险的标准税收文献中一样，最优税收公式仍然可以用标准充分统计来表示。然而，对于私人保险，该公式涉及反映私人市场如何与公共保险相互作用的附加条款。例如，最优税收公式还应考虑资产分配和金钱外部性以及借贷约束的福利效应。