Optimal Financing of Government Purchases

We characterize a planner's optimal allocation of consumption and capital in an overlapping generations model with exogenous government purchases, privately-observed idiosyncratic shocks to the depreciation rate of capital, and a proportional cost of reversing investment to transform used capital to consumption. We show how a package of various taxes and government bonds can finance government purchases and support the same balanced growth path as in the planner's optimum. The optimal tax rate on capital income implements the planner's optimal (but incomplete) sharing of idiosyncratic depreciation risks, while respecting the private nature of these risks.