All modern labour market theories capable of explaining involuntary unemployment as an equilibrium phenomenon imply that increased income tax progressivity reduces unemployment, but they also imply that higher progressivity tends to reduce work effort and labour productivity. This suggests that there may be an optimal degree of tax progressivity where the marginal welfare gain from reduced involuntary unemployment is just offset by the marginal welfare loss from lower productivity. This paper sets up four different models of an imperfect labour market in order to identify the degree of tax progressivity which would maximise the welfare of the representative wage earner. Simulations with these models suggest that the optimal degree of tax progressivity could be quite large, although the results are sensitive to the generosity of unemployment benefits and to the after-tax wage elasticity of work effort