The Ridiculous Rahn Curve

economics, taxes

The Rahn Curve indicates two things.  The first is that there exists a single, optimal level of taxation for maximizing economic productivity.   The second is that this maximum is somewhere between 15-25% of GDP.

The first statement is true.  The second is not.

Here is the Rhan Curve:

Notice the pathetic nature of this graph. No grid, no units and no endpoints. It gives us little information but implies a lot.   It implies that GDP can only grow, not shrink.  It implies that what lies outside of the narrow (?) range covered by the graph is unimportant — nothing to see here citizen.  Let’s improve the graph a little:

Here we show that GDP could rise or fall, and some potential values for the curve near 0% and 100% taxation.

I’ve drawn three potential extensions of the Rhan curve.

If the red extension were correct, then without government (0% government spending), then the economy would collapse (presumably due to lack of police services).  On the other hand, giving government total control of the economy would lead to even more impressive GDP growth than the local maximum that was originally marked as optimal.

If the blue curve were correct, then there would not be much to complain about — just that whoever made the original graph was lazy.  One interesting thing about the blue curve is that the economy would remain the same size with either no government or total government.

Finally, if the green curve were correct, then totalitarianism would lead to economic collapse, and anarchy would lead to prosperity.

Of course, drawing lines on the graph does not tell us anything about what is true about the economy.  However, it does help indicate how poorly conceived the Rhan curve is.

In order to maximize economic productivity, there must be every incentive to produce, and little incentive not to produce.  Why do people work?  To get money.  What do taxes do?  Take away their money.  Taxes are clearly a reason to work less.  The higher tax burden is, the less productive people will be.  The lower taxes, the better.  This is not rocket science.  How low can taxes possibly go…?    Zero!

But wait, government provides services that create an incentive to be productive, namely protection of property.  Government won’t be able to provide protection of property without taxes.  Could it be, that we need to find an optimal balance between State sponsored protection of property and State sponsored violation of property (taxes).

Yes, if government is the only way to provide these services.  Just like only government is able to deliver mail, perhaps only government is able to provide police and courts.

The Rahn Curve conflates two important factors that need to be separated in order to fully appreciate the effect of taxation on economic productivity.  The first is taxes.  The second is protection of private property.  Currently government has used force to steal a large share of the protection market, so it is understandable to associate taxation and protection.  However, by examining these variables independently, we will draw more accurate conclusions about the path to human prosperity.

Higher taxes = lesser growth, lower taxes = greater growth. The exact shape is incidental.

So we can see from this first graph that taxes are inversely proportional to growth.  The more taxes, the less growth.  Taxes bad.

possible relationship between protection of property and economic growth, other things equal

Here we see that more protection of property leads to more growth.  Protection good.

When government provides protection, these two variables become correlated, so that you cannot decrease taxes without decreasing protection, and vice versa.  The relationship is slightly more complicated since taxation is a violation of property itself, but this is the basic idea.

Anyway, because of this correlation you may get an apparent optimal level of taxation for economic growth.  However, it is possible to decouple taxation and protection and then change these variables independently.  You can then lower taxes and increase protection of private property at the same time.  All you have to do is not use taxes to pay for protection.

While we cannot know what these curves actually look like, we know some things about the end points.  At 100% taxation, there is no protection of private property, and thus no economic growth.   In fact, there will be no economy, so the value of the curve at 100% taxation would be -100%, the lowest possible value.

Without government there is always 0% taxation, so economic growth is only correlated to protection of private property.  Will there be 0% protection of private property without government?  Only if everyone becomes a pacifist and takes the locks off their doors (and throws away their guns, gets rid of their dogs, etc).

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