Primer to Logarithmic Taxation Based on Minimum Wage

One of the problems with income tax is the use of income brackets to determine how of a person’s wages should be taxed. Although progressive, these brackets are rigid, arbitrary, and vulnerable to inflation, discouraging people to pursue greater incomes for themselves in order to pay less taxes. Furthermore, such system of taxation requires constant updating to keep up with costs of living and inflation.

Logarithmic taxation seeks to address all these problems by eliminating income brackets altogether and providing a single, smooth, non-linnear, progressive increase to income tax as personal income increases. To make such a system favourable for minimum wage earners, the minimum wage itself would be an integral variable in determine the tax rate.

First of all, the equation for determining the tax rate must be formulated:

Tax Rate = [20 * log (N/M)]%, where

• N = Net 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 20% increase in tax rate.

For purposes of illustration, let us say that the minimum wage is $10 per day. The tax rate of a person earning minimum wage would be as follows:

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

= (20 * log 1)%

= (20 * 0)%

= 0%

Hence, a minimum wage earner has no income tax. Let us now look at a person earning twice the minimum wage ($20):

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

= (20 * log 2)%

= (20 * 0.3)%

= 6%

Net Income After Tax = 20 – (0.06 * 20)

= $18.80

Here, it is shown that a person earning twice the minimum wage loses less than $2. Now, let us see a person earning ten times the minimum wage ($100):

Tax Rate = [20 * log (100/10)]%

= (20 * log 10)%

= (20 * 1)%

= 20%

Net Income After Tax = 100 – (0.20 * 100)

= $80.00

Here, we see a significant portion of income lost ($20), which is the entire wage of the second example. However, the person earning ten times the minimum wage still keeps eight times more money than the minimum wage earner, and he can still afford a comfortable lifestyle.

Now, let us look at someone earning one hundred times the minimum wage ($1,000):

Tax Rate = [20 * log (1000/10)]%

= (20 * log 100)%

= (20 * 2)%

= 40%

Net Income After Tax = 1000 – (0.40 * 1000)

= $600.00

In this example, up to $400 is lost to taxation, forty times the minimum wage, yet the person earning $1,000 still keeps sixty times more money than a minimum wage earner.

Let us turn things up a notch and see how someone earning ten thousand times the minimum wage ($100,000) is taxed:

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

= (20 * log 10000)%

= (20 * 4)%

= 80%

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

= $20,000.00

Here, an astounding sum of money is taxed, and the person still keeps two thousand times more money than the minimum wage earner. To put that into perspective, the minimum wage earner has to work every day for nearly five-and-a-half years to earn that $20,000.

It would be prudent to peg the maximum tax rate at 80% for now because using the same formula indefinitely would eventually result into a 100% income tax, which is absurd. However, the same logarithmic system can be applied recursively to the remaining income after 80% taxation. This will be addressed in a later article.