The Dynamic Welfare Comparison of seignorage Tax and Consumption Tax

This paper compares equilibrium paths and the welfare costs between a seignorage tax along both transitional dynamics and steady state. Using a framework that combines monetary policy with public finance, one of these two taxes is used to finance an exogenous stream of public spending in a fashion to balance the government budget. If only equilibrium paths in a steady state are compared, the welfare cost of a consumption tax is lower. However, if we consider the welfare costs along the transitional dynamics, the result is reversed. The welfare cost of a consumption tax is always higher on the condition of lower relative prices of consumption (to investment) in a seignorage tax than in a consumption tax in early periods of tax changes. In permanent taxes, the condition is that a fraction of investment is cash constrained. In temporary taxes, there is no such a requirement of cash constraints on investment because they create a wedge in the marginal rate of substitution before and after the policy is terminated. This welfare ranking order holds true not only in an optimal growth model but also in an endogenous growth model no matter what the labor supply is inelastic or not.