Optimal indirect and capital taxation

We consider an environment in which agents' skills are private information and follow arbitrary stochastic processes. We prove that it is typically Pareto optimal for an individual's marginal benefit of investing in capital to exceed his marginal cost of doing so. This wedge is consistent with a positive tax on capital income. We also prove that it is Pareto optimal for the marginal rate of substitution between any two consumption goods to equal the marginal rate of transformation. This lack of a wedge is consistent with uniform taxation of consumption goods within a period.