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Thanks for your excellent work! I have revised the paper and letters following your instruction. I just make a little change. Would you please, if it is ok, help me to revise the following 254 words? Of course, I will pay for it, if it is too much as a quick revise:
In a model with a continuum of imperfectly substitutable laborers and endogenous skill premiums, this paper derives optimal tax formulas as a function of social welfare weights and a small set of estimable statistics. It first demonstrates that under an additively separable utility, differential capital tax, basing on capital's effect on skill premiums, is desirable, while nonlinear capital tax is not desirable. The paper then explores both uniform and sector-specific capital income tax (UCIT and SCIT), where sector is identified by the type of laborer working in it. Top labor income tax as well as the top SCIT rate are provided. Numerical application to U.S. taxation delivers an inverted U-shaped relationship between the SCIT rate and sectoral wage. Reform from UCIT to SCIT compresses wage gaps between the top ten percent and others considerably, and especially favors median-income individuals. Their wages are increased by $3.8\%$. Due to production inefficiency, switching from UCIT to SCIT implies a small welfare gains ($%0.07\%\sim 0.22\%$ in consumption-equivalent terms).
Third, we consider additively separable period utility. This assumption abstracts the problem from the interaction between endogenous skill premium and complementarity between consumption and leisure, both of which activate the effects of policy on binding incentive constraints.
A tax or subsidy on initial capital inputs is generally needed to make the tax reform considered in our welfare analysis so that the aggregate capital inputs can jump to the steady-state value at the beginning of period 1. See <cite>werning_optimal_2007</cite> for the reasonability of initial wealth tax and flexible initial capital inputs.
Great work and instruction!