EFA (22): Marginal tax rates

"In this world nothing can be said to be certain, except death and taxes," said American inventor, journalist, printer, diplomat, and statesman Benjamin Franklin, with whom I share a birthday, as I have just discovered.

Taxes are the main method by which governments raise money to finance their spending. One particular aspect of taxes, the concept of marginal tax rates, is the subject of the 22nd item in our Economics for Amateurs (EFA) series. You can find the series here each Monday.

Let's take a simple example. Imagine that a woman, let's call her Lara, earns €100,000 a year in Germany — a very good salary indeed — and pays €50,000 in taxes. (To keep things simple, we'll include as taxes all social insurance payments, such as health, pension and unemployment insurance.)

The next year, Lara gets a pay increase of ten per cent — lucky woman — and thus earns €110,000. Imagine further that her net salary also rises by €10,000 (very unusual for Germany, I admit, but bear with me).

The question is: what is Lara's marginal tax rate in this situation?

The answer is simple: zero. Her gross salary has increased by €10,000 and her tax bill hasn't increased at all. This leads us to an important definition:

• The marginal tax rate is the percentage taken by the government of an increase in earnings.
  

Marginal tax rates are important because they can have an impact on people's incentive to increase their gross earnings by working harder, getting a promotion, taking on extra resopnsibilities, taking risks and innovating. Very high marginal tax rates — such as the 83 per cent top rate that Britain had in the 1970s — can seriously damage incentives.

Many people — particularly on the left — favour very high marginal tax rates for the rich as a way of distributing income. They typically don't believe that the disincentive effects of taxes are very high.

Note, however, that redistribution depends not on marginal tax rates but on average tax rates — that is, on the proportion of their total income that people pay in tax.

In our example, Lara has an average tax rate of 50 per cent before her pay increase (50,000 divided by 100,000 times 100). After the increase, her average tax rate falls to jus over 45 per cent (50,000 divided by 110,000 times 100).

In this situation, we can say that the tax system is degressive at Lara's income level, because the average tax rate falls as income rises. A progressive tax system, on the other hand, is one that has rising average tax rates as income rises — that is, the government redistributes income by taking proportionately more from the rich.

But note again, that this doesn't necessarily require rising marginal tax rates. Even if there were only one tax rate — say, 40 per cent — the tax system would still be progressive if there are tax-free allowances that everyone gets, but which are worth proportionately more to those on lower incomes.