### 18.2 Selecting a linear tax rate

In the graph below, you can now analyze the effects of a freely adjustable tax rate. For comparison, besides the optional tariff (blue), the current tariff 2016 including the solidarity surcharge (red) and the inflation-adjusted tariff 1965 are shown. The marginal tax rates are shown with a solid line, the average tax rates are shown dashed. In the upper graph, taxable incomes up to 100,000 Euro are shown, in the lower graph up to 500,000 Euro.

In the current version, the tax rate has only three zones: the tax-free subsistence minimum, the linear progression zone and the proportional zone. In the progression zone, there is a rising marginal tax rate, i.e. each additional Euro is taxed higher than the one before. In the proportional zone, a constant marginal tax rate applies, i.e. every additional income is taxed at exactly this rate. The zones can be set by moving the points ${T}_{\mathit{start}}$ and ${T}_{\mathit{max}}$. With the button ’update values’ you can also set exact values. The thresholds cannot become negative and ${T}_{\mathit{max}}$ is only effective above ${T}_{\mathit{Start}}$.

Besides the comparison of the average burden, the tax revenue is given below as a benchmark. This way, it can be judged whether a tariff change is revenue neutral or generates more or less revenue. The comparison of the average tax tariffs (dashed curves) serves to judge the effect of a new tariff. These show for which incomes the current burden is higher or lower. One can see, for example, that the 1965 tariff for low incomes represents a much higher burden than the current one, since the green curve is above the red curve.1 The distance between the two curves indicates in percent by how much the old tariff (green) burdens the taxpayers more than the current one (red). With a taxable income of approx. 30,000 Euro, the two curves intersect and the red curve is on top, i.e. incomes above 30,000 Euro are currently burdened more than would be the case with the real tariff of 1965. For a taxable income above 140,000 Euro, the relation reverses again, as can be seen in the lower graph. Middle incomes have thus been burdened more since 1965, while low and, especially, high incomes have been relieved. In the same way, the effects of the self-selected tariff (blue) can now be analyzed in comparison to the others.

It can be seen that the exemption limit has an enormous influence on the tax revenue. If you increase it to 10.000, the total tax revenue is reduced by about 10%. Possible revenue-neutral changes would be (a) a threshold tariff, i.e. for a taxable income above 19,000 a tax rate of 50%, (b) ${T}_{\mathit{start}}$ = 10.000 and 20% and ${T}_{\mathit{max}}$ = 55.000 and 50%, and (c) ${T}_{\mathit{start}}$ = 10.000 and 25% and ${T}_{\mathit{max}}$ = 85.000 and 50%. It can be seen that the exemption limit has an enormous influence on the tax revenue. If you increase it to 10.000, the total tax revenue is reduced by about 10%. Possible revenue-neutral changes would be (a) a threshold tariff, i.e. for a taxable income above 19,000 a tax rate of 50%, (b) Tstart = 10,000 and 20% and Tmax = 55,000 Euro and 50% and (c) Tstart = 10,000 and 25% and Tmax = 85,000 and 50%. The large effect of a change in the basic tax rate or exemption limit is mainly due to the effect on the tax rates of middle incomes, which account for the largest part of tax payments. If the upper limit is shifted so diagonally upwards that the tax rates of middle incomes do not change, the effect is very weak. This shows that the creditability and deductibility of income is in fact more important than the top tax rate, although in the political debate it seems to be the other way around.

Basic tax rate ${T}_{\mathit{start}}$(Y-Wert) %      Tax free allowance ${T}_{\mathit{start}}$(X-Wert) Euro
Maximum tax rate ${T}_{\mathit{max}}$(Y-Wert) %      Start of upper tariff zone ${T}_{\mathit{max}}$(X-Wert) Euro

1This is due to the higher limits for the tax-free subsistence level enforced by the Federal Constitutional Court.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de