The Optimum Quantity of Capital and Debt

In this paper we consider an optimal taxation problem in an incomplete markets model to study the optimal quantity of capital and debt. The government commits itself ex-ante to a tax schedule and government debt. In contrast to most of the existing literature these instruments are chosen to to maximize agents' discounted present value of lifetime utility. Whereas the literature mainly focuses on characterizing the steady state which maximizes welfare, we characterize and compute the optimal policy along the full transition path. In particular our characterization takes into account that the optimal long-run policy depends on capital, debt and taxation during the transition path. We show theoretically that it is optimal to equalize the pre-tax return on capital and the rate of time preference in the long-run, i.e. the capital stock satisfies the modified golden-rule. Quantitatively we find that the tax on capital is around 3 percent in the long-run. Labor is taxed at a much higher rate where the precise number depends on the labor supply elasticity. For standard choices for this elasticity we find a labor tax rate of almost 40 percent to be optimal in the long-run. The reason for such a hight tax rate on labor income is that labor income is risky. Taxing this risky income and redistributing it back through lump-sum transfers improves ex-ante welfare in the long-run. Transfers and the optimal level of debt along the transition are chosen to equalize the amount of redistribution over time. Initially capital is taxed higher than in the long-run since it is inelastically supplied whereas labor is taxed less than in steady state.