Impacts of Labor Taxation with Perfectly and Imperfectly Competitive Domestic Labor Markets under Flexible Outsourcing

What are the impacts of labor tax reform on wage setting and employment to keep the relative tax burden per low-skilled and high-skilled workers constant in the case of heterogenous domestic labor markets, i.e. imperfect competition in low-skilled labor and perfect competition in high-skilled labor in the presence of outsourcing? A higher degree of tax progression by raising the wage tax and the tax exemption for the low-skilled workers will decrease the wage rate and increase labour demand of low-skilled workers, whereas it will decrease (increase) employment of high-skilled workers in CES utility function when the elasticity of substitution between consumption and leisure is higher (lower) than one. A higher degree of wage tax progression for the high-skilled worker will have no effect on the high-skilled wage in the presence of CES and C-D utility function so this will have no total employment effects.