Supply-side Optimal Capital Taxation with Endogenous Wage Inequality

In a model with a continuum of imperfectly substitutable laborers and endogenous skill premiums, this paper derives optimal tax formulas as functions of social welfare weights and a small set of estimable statistics. It first demonstrates that differential capital tax, based on capital's effect on skill premiums, is desirable even in the steady state, while nonlinear capital tax is not desirable under an additively separable utility function. It then explores both uniform and sector-specific capital income tax (UCIT and SCIT), with a sector corresponding to a type of laborer. Numerical application to U.S. taxation delivers an inverted U-shaped relationship between the SCIT rate and sectoral wage. The optimal SCIT rate on the top-income sectors increases with the elasticity of substitution between the sectoral products and amounts to a net return tax of 45.9%. Reform from UCIT to SCIT compresses wage gaps between the top ten percent and others considerably. It especially favors the median-income individuals whose wages are increased as high as 3.8%. Due to production inefficiency, switching from UCIT to SCIT implies small welfare gains (0.07%∼0.22% in consumption-equivalent terms)