Month: December 2014

Logarithmic Taxation Beyond 80%

Previously, we have tackled tax rates on individuals with income taxes up to ten thousand times the minimum wage. Pegging the maximum tax rate at 80% is crucial because further progressing would eventually lead to a tax rate of 100%. However, there is a way to continue making progressive taxation beyond ten thousand times the minimum wage.

For any person earning more than ten thousand times the minimum wage, the tax rate is automatically 80%. However, the remaining income would be subject to another tax described in this formula:

Second Tax Rate = [20 * log (A/2000M)]%, where

  • A = net income after taxes
  • M = minimum wage
  • The calculated value is rounded down to the lower tenth of a percent

Here, 2000 was used as the coefficient for M because that would be the net income after tax of someone earning ten thousand times the minimum wage, which is the minimum value to obtain a tax rate of 80%.

Let us look at someone earning ten thousand times the minimum wage ($100,000 at $10)

Tax Rate = [20 * log (100000/10)]%

= (20 * log 10000)%

= (20 * 4)%

= 80%

Net Income After Tax = 100000 – (0.80 * 100000)

= $20,000.00

Second Tax Rate = [20 * log (20000/20000)]%

= (20 * log 1)%

= (20 * 0)%

= 0%

It can be seen that someone earning exactly ten thousand times the minimum wage will not be subject to the second tax rate. Let us now look at someone earning one million times the minimum wage ($10,000,000):

Tax Rate = 80%

Net Income After Tax = 10000000 – (0.80 * 10000000)

= $2,000,000.00

Second Tax Rate = [20 * log (2000000/20000)]%

= (20 * log 100)%

= (20 * 2)%

= 40%

Net Income After Second Tax = 2000000 – (0.40 * 2000000)

= $1,200,000.00

Even with an additional 40% second tax on top of the 80% tax, less than 90% of income was deducted, and a large sum of money is still kept.

Yet at sufficient quantities, the second tax rate can approach 80% and it has to be pegged there again. A third tax rate can be introduced in the same manner:

Third Tax Rate = [20 * log (A/4000000M)]%, where

  • A = net income after taxes
  • M = minimum wage
  • The calculated value is rounded down to the lower tenth of a percent

Let us look at a person earning an improbable one billion times the minimum wage ($10,000,000,000):

Tax Rate = 80%

Net Income After Tax = 10000000000 – (0.80 * 10000000000)

= $2,000,000,000.00

Second Tax Rate = 80%

Net Income After Second Tax: 2000000000 – (0.80 * 2000000000)

= $400,000,000.00

Third Tax Rate = [20 * log (400000000/40000000)]%

= (20 * log 10)%

= (20 * 1)%

= 20%

Net Income After Third Tax = 400000000 – (0.20 * 400000000)

=$320,000,000

Here, so much money has been taxed, but $320,000,000 was still kept, which is 32,000,000 times the minimum wage.

If a person earns a googol or even a googolplex times the minimum wage, this recursive pegging at 80% and constant reapplying of the logarithmic formula will work because nobody is every taxed at 100%. All net incomes after all taxes will always increase. Hence, this system of taxation is progressive until infinity.

 

Logarithmic Taxation on Corporations

Logarithmic taxation based on minimum wage may apply not only to individuals but to corporations as well. Because corporations earn a lot more than individuals, corporations would tend to have a larger tax rate than individuals given the same equation, which would unduly cripple corporations of necessary capital. However, an equation more suited for corporations would not look so different than the one originally used for individuals:

Tax Rate = [5 * log (W/M)]%, where

  • W = net corporate income before taxes
  • M = minimum wage
  • The calculated value is rounded down to the lower tenth of a percent

Using this formula, every ten-fold increase in income above the minimum wage would result in a 5% increase in tax rate instead of 20% seen in individuals.

For example, we look at a corporation earning ten thousand times the minimum wage (at $10 minimum wage, that would be $100,000):

Tax Rate = [5 * log (100000/10)]%

= (5 * log 10000)%

= (5 * 4)%

= 20%

Net Income After Tax = 100000 – (0.20 * 100000)

= $80,000.00

In a previous example, an individual with the same net income would be taxed at 80% and keep only $20,000.

For a corporation to be taxed at 80%, it would have to earn a staggering ten quadrillion times the minimum wage ($100,000,000,000,000,000):

Tax Rate = [5 * log (100000000000000000/10)]%

= (5 * log 10000000000000000)%

= (5 * 16)%

= 80%

 

At this point, it would be impractical to compute for the net income after taxes because no corporation would have a net income of ten quadrillion times the minimum wage.

How will this affect policy making? Whenever there is an increase in the minimum wage, corporations suffer because they are able to hire less workers, resulting in higher unemployment rates. However, using this method, increasing the minimum wage would effectively lower corporate taxes, increasing their capability to hire more employees. Consequently, increasing the minimum wage would have a smaller impact on unemployment.