Supply-side optimal capital taxation with endogenous wage inequality

•We study supply-side optimal capital taxation with endogenous wage inequality in a general equilibrium Mirrlees (1971) economy with a continuum of heterogeneous laborers. We allow for arbitrary complementarity or substitutability between capital inputs and different kinds of labour inputs. Thus, relative wages endogenously evolve with the accumulation of capital. Under this setting, we study both uniform capital income tax (UCIT) and sector-specific capital income tax (SCIT) and demonstrate interactions between optimal labor and capital income taxes.•We first demonstrate 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.•We then show that a type of capital should be taxed if skill premium increases with the accumulation of the capital. Otherwise, it should be subsidized. Moreover, we find that SCIT is generally needed to implement the second-best allocation, which means that optimal capital tax rate varies with sectors (industry or firm) and full production efficiency is not optimal. If sectoral wage increases with the sectoral capital input, optimal SCIT is positive (negative) for the high-income (non-high-income) sectors.•A numerical application to U.S. taxation is provided. The optimal UCIT rate on equipment capital amounts to a net return tax rate ranging from 24.1% to 36.5%. This is lower than the effective tax rate in the United States (37.1%). However, the top SCIT amounts to a net return tax of 45.9%. Interestingly, there is an inverted U-shaped relationship between the SCIT rate and the sectoral wage. The higher the elasticity of substitution between skills, the higher (lower) the SCIT on the top-income (lowest-income) section.•Switching from UCIT to SCIT is done to compress wage gaps between the top ten percent and the others. It especially favors the median-income individuals whose wages are increased as high as 3.8%. Meanwhile, the labor demand is increased by 1.7%~5.1%. Due to production inefficiency, switching from UCIT to SCIT implies small welfare gains (0.07%∼0.22% in consumption-equivalent terms).