Zero Tax Economics - The Equation

I've done more thinking about my Zero Tax proposal and, as a result of studying how the money multiplier works in factional reserve banking, I believe that my proposal has a very good chance of working.

To summarise:
  1. Government removes all taxes - income tax, sales tax, corporate tax... all of it.
  2. Government spending is funded by money creation - seigniorage. The Central bank creates this money for the government.
  3. To prevent inflation, the Central Bank increases the Reserve requirement and applies it to M3 - the broadest money supply.
The most common critique I had of this proposal was that increasing the reserve requirement would not stop inflation, and that, as time increased, the reserve requirement would approach 100%. These discussions can be found at Angry Bear and at Megan McArdle's blog (the latter with the heading "craziest idea I have ever heard"!).

Despite the fact that this idea is so radical that people think it "bonkers" (as one commentator at Megan McArdle's blog describes it), I have tested the idea against the actual equations contained in the money multiplier - and it works. In other words, it is possible for the Central bank to create money out of thin air to fund government spending and still maintain zero/low inflation with an elevated reserve requirement.

Here is the equation:

RM3 = "Reserve requirement on M3" - the reserve requirement needed to maintain zero/low inflation.
G = Government Spending
GDP = Gross Domestic Product
r = Current reserve requirement on M1
M1 = M1 narrow money supply (currency+deposits)
M3 = M3 broad money supply

To put it simply, when the central bank creates money for government spending, the money created is equivalent to a percentage of GDP. In order to remove any inflationary effects of this money creation, the reserve requirement increases by this same percentage. If government spending is 20% of GDP (as is the case in the USA) then the Reserve requirement on M3 needs to be 20%, plus the reserve requirement already in place on M1.

Now for a short explanation of how the money multiplier works. Here is the equation:

Whereby m is the multiplier and R is the reserve requirement. If the reserve requirement is 20%, then R looks like this:

Which means:

Which in turn means that when the reserve requirement is 20%, then the money multiplier is 5. If the central bank creates $100, then the total amount of money created through commercial bank money creation will be $500.

But when money is created by seigniorage, the amount created at the beginning increases. If we retain the current model of $100 central bank money and a 20% reserve requirement, and then add to it the relative size of the US government (20% of GDP), then we are increasing the central bank money to $200.

So if the reserve requirement increases to 40%, then R looks like this:

Which means:

Which in turn means that when the reserve requirement is 40%, then the money multiplier is 2.5. If the central bank has created $200, then the total amount of money created through commercial bank money creation will be... $500.

Yep, that's right, the same amount as before. Even with creating twice the amount of money, reducing the money multiplier by increasing the reserve ratio ensures that no inflationary pressures will ensue.

As I pointed out before, this taxless system is not a "free lunch" - the tax burden remains in the form of higher market interest rates. Moreover, the larger the government is in proportion to the economy as a whole (Around 20% for the US, 34% in Australia, 53% in Sweden), the higher the market interest rates will be.

As a monetary tool, the reserve requirement has become outdated. Many countries (including Australia) have a zero reserve requirement, preferring to use central bank interest rates. In the taxless system I propose, the reserve requirement would be solely for the purpose of balancing out government spending, which means that current reserve requirements must be dispensed with. This, of course, means that the last part of my Zero Tax equation (the first diagram) about the reserve requirement on M1 divided by M3 can be dispensed with in economies that do not currently run a reserve requirement.

In a simple sense therefore, the reserve requirement on M3 - the percentage amount - is identical to the percentage of GDP that government spending takes up.

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