Tax rate

The marginal tax rate (marginal tax rate ) is the rate at which the respective nearest unit of the tax base will be charged. It indicates what proportion of additional taxable euros, dollars or something else must be dissipated as a control.

Has practical significance for the marginal tax rate associated with progressive income tax rates, as they are the world (including Germany, Austria and Switzerland ) use. Here, the marginal tax rate on the amount of total taxable income ( tax base ) is dependent. Within the limits of the basic allowance it is equal to zero, then it increases the rate of tax to the top tax rate. Also a top earner pays only a part of his income the top tax rate, however, to other parts of lower or to basic allowance no tax. Looking at all the pieces together, we obtain an average tax rate, which is always lower than the top rate.

The marginal tax rate is (only ) relevant to the question whether it is worthwhile to increase the taxable income or ( by operating expenses, advertising costs or other allowances) to decrease.

Introduction Example

The taxable annual income of an unmarried taxpayers is € 60,000. According to the example shown in the picture above right are € 11,250 to pay income tax. These are 18.75% of taxable income ( = average tax rate ). The marginal tax rate is calculated by considering the income growth.

Any increase in the taxable income of 3,000 € to 63,000 €, so a total of € 12,322.50 to pay income tax. On these income gains of € 3,000 is therefore unnecessary income tax of € 1,072.50, thus 35.75 %. That would be the " differential tax rate ". If we now consider very small changes in income with respect to the amount of tax function, one obtains the marginal tax rate. This is so called because he is right on the border to the next additional euro earned. Thus, the marginal tax rate in the example of the salary increase is initially 35 %, but 36.5%.

It can be seen that the marginal tax rates differ from the difference tax rate, which, however, can be neglected at low income growth.

Definition

Mathematically, it is the marginal tax rate by the derivative ( the derivative) of the amount of tax function. If the amount of tax function is differentiable at a certain value of the tax base, so its derivative is the marginal tax rate.

With = marginal tax rate and = tax base ( taxable income ) the following relationship:

This is also the slope of the amount of tax function in the considered value of the tax base.

Also, the input and the top tax rate are, by definition, marginal tax rates. The rate of tax refers yes only on the income portion above the basic personal allowance. The top tax rate will be charged only for the income part above the top Einkommenseckwert, from which it qualifies.

Germany

The profile of the marginal tax rate as a function of taxable income ( DAS ) is derived from the adjacent graph showing the historical development.

The income tax rate in Germany is a linear- progressive scale, but practically corresponded with those in force until 2003 rounding as a step amount tariff. The levels of income were € 36 wide; caused by the passing of each stage, additional tax burden was about 7 to 18 €. The marginal tax rate or better differential tax rate therefore was about in 7/ 36 = 19.4% and 18/ 36 = 50%.

Since 2004, the tax amount is significantly increased continuous, but is rounded to the nearest euro amounts. The corresponding width of the levels of taxable income ( DAS ) is thus only 2-5 euros.

Example

The taxable annual income of an unmarried taxpayers is € 45,000. After the tax rate in 2010 of which € 10,870 income tax to be paid. This corresponds to an average tax rate of 24.2 % of taxable income.

Increases the taxable income by 3 to a total of € 45.003 € so is because of rounding exactly one euro to pay more income tax. This corresponds to 33% of the increase in income. This is the marginal tax rate in this case. Due to the rounding rule but caution is advised. Rises namely the income of 45,000 Euros to 45.002 Euros only, then the tax amount remains the same and the marginal tax rate would be 0%. Therefore it is better to speak of the differential tax rate and consider greater income disparities.

With an income increase of 450 Euros per year, which corresponds to a salary increase of 1 %, resulting in a differential tax rate of 38.44 %. By comparison, the calculated means of differential quotient marginal tax rate at 45,000 euros is 38.39 %, at 45,450 euros he is 38,60 %. This small difference can therefore be neglected in practice.

What is the change in the tax burden in an increase or decrease of income by a certain amount, is determined by the marginal tax rate and results from the adjacent table.