This paper analyses wage inequality and the welfare effects of changes in capital and labour income tax rates for different types of agents. To achieve this, we develop a model that allows for capital–skill complementarity given non‐uniform distributions of asset holdings and labour skills. We find that capital tax reductions lead to the highest aggregate welfare gains but are skill‐biased and thus increase inequality. However, our analysis also shows that the inequality effects of capital tax reductions are lower over the transition period compared with the long run.