Scale-dependent and risky returns to savings: Consequences for optimal capital taxation

I present a model of optimal capital taxation where agents with heterogeneous labor productivity randomly draw their rate of return to savings. Because of scale dependence, the distribution of rates of returns can depend on the amount saved. Uncertainty in returns to savings yields an insurance rationale for taxing capital on top of labor income. I first show that, because of scale dependence, agents making the same saving decision should access the same rate of return at the optimum. I then constrain the information set of the government and show that, as soon as return are uncertain, positive capital income taxation is needed at the optimum. The optimal linear tax on capital income trades off insurance with distortions to both savings and to the rate of return in a context of scale dependence. Eventually, I argue that scale dependence in and of itself is not sufficient to justify capital taxation on top of labor income taxes. These results are still valid when agents can optimize between a risk-free and a risky-asset that can both exhibit scale dependence.