# B3 Lump Sum Tax Reform

## B3.1 The Tax Postponement Effect

Suppose that the government changes the combination of lump sum taxes (T^{1}, T^{2}) in period j + 1. T^{2} is raised and T^{1} is reduced. This yields:

First, let us investigate the partial equilibrium effect of tax reform on the present value of the lifetime tax payment T. If r > n, postponing tax payments to later in life (T^{1} ! t^{2}) means a reduction of the lifetime present value of taxation. This is the so-called the tax postponement effect.

For future generations, j + 1+i (i = 1, 2, ...) for Eq. (9.B5^{0}) means that the present value of tax payments, T, decreases if and only if r> n. If r> n, this gives an extra benefit to the future generation. If r < n, the tax postponement effect is unfavorable for the future generation.

For the existing younger generation j + 1, the tax postponement effect works in the same way as with the future generation. The tax postponement effect is relevant to the steady state and the transition process. For the existing older generation j, T?_{+}1 is increased, while T? is not reduced. Thus, the lifetime present value of taxation Tj is raised. This corresponds to the third term of Eq. (9.B5^{0}) and gives an extra burden to generation j. The result may be called the direct tax reform effect or the time horizon effect.

During the transition, the earlier generation may suffer significant reductions in welfare because of the tax reform. Note that this effect works irrespective of whether r is greater than n or not. In this sense, the effect should be distinguished from the tax postponement effect.