Nonlinear Income Tax

The First Best

So far, we have considered the linear income tax schedule. The marginal tax rate is constant there. This tax schedule is called a flat tax. In the real economy, tax reforms that reduce the degree of progressivity have been enacted in several developed countries such as the US and the UK. Further, some East European countries have recently adopted a flat tax rate. However, most countries, including Japan, adopt a nonlinear progressive tax whereby the marginal tax rate increases with income. Theoretically, if the government can impose nonlinear tax rates freely, what is the optimal tax schedule?

Imagine that a step-wise nonlinear tax schedule with flat tax rates is available, as shown in Fig. 10.9. This schedule could be optimal in some instances. In this figure, person L faces a flat tax schedule around point TL and person H faces a flat tax schedule around point TH. At these points, the marginal tax rates for L and H are both zero; namely, the slope of the tax schedule at TH and TL is zero; hence, the tax burden does not rise marginally with income.

Note that the marginal tax rate corresponds to the size of efficiency cost. If the marginal tax rate is zero, the excess burden disappears; hence, the issue of an excess burden in terms of efficiency does not arise. Moreover, as shown in Fig. 10.9, person L receives a subsidy while person H pays tax. Since income is actually

The optimal tax schedule

Fig. 10.9 The optimal tax schedule

redistributed from the rich to the poor, this is also desirable from the viewpoint of equity.

If the government redistributes income at zero marginal tax rates, it must impose a nonlinear tax, not a linear income tax. This type of nonlinear, step-wise optimal tax may be regarded as the imposition of a lump sum tax on person H and the transference of a lump sum subsidy to person L. This could be called an ability- specific lump sum tax and is the first best tax schedule to attain the first best without sacrificing efficiency costs.

Such a schedule imposes a lump sum tax, TH, on person H and transfers a lump sum subsidy, TL, to person L. Thus, we have

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