Income Tax Loads - Soaking the Rich?

The other day I was listening to the radio of a well known conservative talk show host. One caller brought up an interesting topic - the Federal income tax load. The key point he was trying to make was that the higher income taxpayers pay the higher percentage of the Federal income tax load. I decided to do little more research.

I found out that was a common claim and it goes like this (for the year 1997 as an example) :
1. The top 1% of income earners pay 33.2% of the total income tax load.
2. The top 5% pay 51.9% of the total income tax load.
3. The top 10% pay 63.2% of the total income tax load.
4. The top 25% pay 81.7% of the total income tax load.
5. The top 50% pay 95.7% of the total income tax load.
6. The bottom 50% pay only 4.3% of the total income tax load.

The basic claim seems to be true. It sure looks like we are hitting the rich a lot harder than we should. However there are those that like to point out that those numbers give the wrong impression. The counterexample goes as follows:

Imagine a population of 10 people - 9 earning $10,000 and 1 earning $100,000. The breakdown for income would be:

• The total amount of income is $190,000.
• The bottom 90% of income earners make (90/190)*100 = 47.4% of the total income
• The top 10% make 52.6% of the total income.

Let's say the tax rate for the $10,000 earners is 10% and for the $100,000 earner is 20%. Then the tax load will become:

• The total amount of taxes is $29,000.
• The bottom 90% of taxpayers carry (9/29)*100 = 31% of the tax load.
• The top 10% of taxpayers carry 69% of the tax load.

From the percentages alone, it sure looks like the top 10% of earners carry an unfair amount of the tax load. However, their claim is that the top 10% still get to keep $80,000 while the remaining 90% of tax payers still only get to take home $9,000. They are also concluding that the huge disparity of an income difference of 10 times between the high and low income is what causes the numbers to be what they are. Keep in mind that I am using a simplified model here - only one tax. In reality of course, there are far more kinds of taxes with far more complications but I am analyzing the claims being made based on pure numbers alone.

Well, I get the point of the example and it is a good counterpoint. However, would it stand up to further analysis?

The fact is that, the population is not properly represented by an example of 10 people. An example of 100 would be fairer or even 1000 or 10,000. So, I broke out the spreadsheet and made a population of 10,000 that had:

• a uniform distribution of incomes from $10,000 at the bottom to $1.4 million at the top.
• a tax rate of zero up to $15,000
• a tax rate of 5% up to $30,000
• a tax rate hike of 1% per $10,000 topping out at 40% from $370,000 on up.

The experimental results were:

• The top 1% income earners made an average of $1.45 million
• The top 5% income earners made an average of $1.31 million
• The top 10% income earners made an average of $1.16 million
• The second 10% income earners made an average of $707,000
• The third 10% made an average of $429,000
• The fourth 10% made an average of $260,000
• The fifith 10% made an average of $157,000
• The remaining 10% tiles made $96,000 - $58,000 - $35,000 - $21,000 and $13,000 respectively.
• The top 1% earners carried 5.53% of the tax load.
• The top 5% earners carried 25.1% of the tax load
• The top 10% earners carried 44% of the tax load
• The second 10% earners carried 27% of the tax load
• The third 10% earners carried 16.2% of the tax load
• The fourth 10% earners carried 7.25% of the tax load
• The fifth 10% earners carried 2.81% of the tax load
• The remaining 10% tiles carried 1.12, 0.47, 0.21, 0.10 and 0.014% respectively

What this tells me is that the 11 person example is not a good counterpoint to the initial claim such as that using the 1997 figures above. Looks like we need to look at actual incomes to see how "fair" the initial claim is. We do know that the counterpoint has a real problem though.