# Increasing tax rates may not… increase taxes!

If governments face a budget deficit that is deemed to be too high, two actions can be taken: government spending is lowered, or government income is increased. The lion’s share of government income comes from taxes; increasing government income as a way of reducing budget deficits therefore translates to increasing taxes. But taxes are not increased, really; tax rates are increased.

But what few people know is that in certain situations raising tax rates will actually reduce government income from taxes.

To understand why, let’s start with the following graph, featuring a country with a GDP of €100.

Let’s assume that taxable income is therefore equal to €100. Government can now tax this taxable income. Let’s say that the tax rate was equal to 30%, thus giving the government an income of €30. By this logic, if taxes were to be increased by 5% to 35%, government income would increase with €5 to €35. This seems intuitive: if taxes rates are raised, government income will rise accordingly.

However, there is a wrong assumption: the line of taxable income is not fixed at €100. In fact, it is not a straight horizontal line. It is good to realise here that tax rates are chosen before taxable income materialises. That is to say, if the government decides that next year’s tax rate equals 30%, it does not know whether the taxable income will equal €100, €95, or €105. There’s a time lag between deciding a tax rate, and the actual act of taxing.

Let’s consider a 100% tax rate, at the far right of the graph. If a government communicates that it will tax all taxable income at a rate of 100%, it may be clear that (economically) it would make no sense for people to earn an income – they have to give it away entirely. A 0% tax rate, alternatively, would imply that the government would practically have no income at all, and thus not exist. It seems impossible to imagine a thriving economy without any kind of government. Let’s adapt the graph a bit:

So, taxable income is not fixed, and it’s not unrelated to the chosen tax rate. Probably, the actual graph looks something like this:

Government income is equal to the tax rate times taxable income. This boils down to the surface of the coloured square in the graph below. In this case, government income would equal €105 times X%.

If income from taxes is to be maximised, the trick is to maximise the size of the coloured square. If we choose a higher tax rate, we see that the square becomes wider. Regarding the last graph this would initially raise government income, because even taxable income would increase if tax rates were to be increased. Moving further along the graph, government income increases until the peak of the graph because the square gets both higher and wider. Past the peak, the square still becomes wider, but slowly it starts to decrease in height. At a certain point, the square attains a maximal size. After this point additional tax rate increases would decrease the square’s size, because taxable income would decrease more than tax rates would increase. The three graphs below illustrate this.

This can be translate into yet another graph, which shows government income as raised from taxes:

Increased tax rates initially raise government income, until X%. After this, raising tax rates will decrease tax income. The consequence is that tax rate increases will only result in additional government income if the tax rate in the status quo is below X%. The example above treated a simple example of one country with one tax rate. The logic behind it can, however, be applied to numerous situations in which governments tax people, companies, products, etc.

The Dutch government, or at least some of its officials, do not seem to fully understand the logic behind it. Two examples show that tax rates were raised to increase government income, but failed to do so because the tax rate was already higher than the X% of the example above:

(1) The Dutch government raised the tax rate for the highest tax bracket to 52%. The Netherlands Bureau for Economic Policy Analysis concluded in a report that this would not yield the desired results, because the government income maximising tax rate was 49%. In this case, raising the tax rate past 49% would lower the taxable income for several reasons. Firstly, the direct incentive for people to earn income would be weaker, since they would have to give up more of it to the government. Secondly, illegal tax evasion would become more alluring since its benefits become greater. Thirdly, legal tax evasion would become more alluring. An example of the latter, albeit in a different situation, is Gérard Depardieu, a French actor that left France for Russia because he refused to pay taxes at a 75% rate.

(2) In order to increase government income, the Dutch government published plans to increase fuel taxes. Increasing these fuel tax rates would, though, have some adverse effects the government had not taken into account (or at least not enough). Firstly, increasing these tax rates would increase the price of fuel, and therefore the costs of transport. Companies using transport would therefore see their incomes decrease, resulting in a lower taxable income. Secondly, people who nowadays get fuel at Dutch gas stations might decide to cross the border and get fuel in Belgium or Germany, where gas prices are already lower. Income for gas stations would decrease, lowering taxable income. Some say that the decrease in income for gas stations would be as high as €560 million. This amount may even be higher if those who drive across the border for fuel spend more money there as well, for instance on groceries. Other sources indicate that no less than (a probably exaggerated, but still) 800 gas stations that are situated close to the borders with Germany and Belgium will be threatened in their survival. A significant share of them going bankrupt will obviously lead to a lower taxable income. Thus, raising tax rates may actually, eventually, lower government income froms taxes

Equally interesting is the observation that lowering tax rates may actually lead to increased government income out of taxes. Perhaps a topic for a future post…