Tax Brackets III

 

Do You Hear The People Sing

Do you hear the people sing?
Singing the song of angry men?
It is the music of the people
Who will not be slaves again!
When the beating of your heart
Echoes the beating of the drums
There is a life about to start
When tomorrow comes

Fool me once shame on me.  Fool me twice shame on you.

In an ideal world, the income tax debate would go like this. What is the lowest acceptable income tax rate. The Bible might call this a tithe, 10%. If that is the lowest rate, then according to the laws of normal distributions, the mode/mean/median rate should be 20%, and the highest rate should be 40%. The Tax Cut and Jobs Act, TCJA, sets the lowest tax rate at 10% and the highest tax rate at 37%, which is not exactly normal, but is arguably close enough. It also confuses marginal tax rates and effective tax rates, but that will be discussed later.

The question is how to transition from a rate of 10% to a rate of 37% in a fair manner. One suggestion might be to pick an arbitrary amount and transition at that income. However establishing that transition income would be contentious politically, but mathematically it should be such that the median tax rate is paid by the median income.  Since it is a tax on income, not a tax on individuals, if income is not normally distributed among individuals, then arguably the transition should follow the distribution of income not people. The distribution of income is not normal (a statistical term, not an ethical term). If incomes were distributed normally, then the mean would be equal to the median would be equal to the mode, the most common value. According to the US Census for income, the mean is definitely not the median. One of the most common non-normal distributions is the exponential distribution. Without debating why incomes are not normally distributed, the transition from the lowest tax rate to the highest tax rate should arguably follow this existing distribution of income. (Interestingly, a flat tax also implies that everyone has the same income. To be mathematically consistent, those that argue for a flat tax must also be also communists who argue that every individual should have the same income.)

Any non-linear distribution can be approximated by a series of straight lines of EQUAL intervals, which is how calculus works. There are seven brackets in the TCJA. Assuming that the top bracket is the full amount, and the first bracket is the lowest amount, then there are five brackets in which to make the transition (e.g. the total tax paid in the highest income in the sixth of seven brackets should have an effective rate of 37%, the highest rate). The effective tax rate at any income x is 10% + 27%*(1-e^-λx), where 1/λ is the mean income according to the exponential distribution. This can be approximated by a series of straight lines, tax brackets, as:

a=λ*10%= 10% λ
b=λ*(10% + (1-e^-.2)) = 28.1% λ
c=λ*(10% + (1-e^-.2) + (1- e^-.4)) = 61.1% λ
d=λ*(10% + (1-e^-.2) + (1-e^-.4) + (1-e^-.6)) = 106.2% λ
e=λ*(10% + (1-e^-.2) + (1-e^-.4) + (1-e^-.6) + (1-e^-.8)) = 161.3% λ
f= λ*(10% + (1-e^-.2) + (1-e^-.4) + (1-e^-.6) + (1-e^-.8) + (1-e^-.1) ) = 224.5%  λ

This means that the tax brackets are a simple problem given the highest tax rate, 37%, the lowest tax rate, 10%, and the number of brackets, in this case seven. The only variable in the table above that needs to be specified is the mean income. This should be computed for each tax filing using the tax status (e.g. Single, Married Filing Jointly, Married Filing Separately, Head Of Household, etc.). As an example, the US Census specifies the mean household income as $102,316 in 2021 according to Income in the United States: 2021: Current Population Reports. With this amount, and the actual percentages substituted in place of the exponential equations, the table would be: 

Bracket	Lower income	Upper Income	Fixed Tax	Marginal Tax Rate  (on amount above lowest income in bracket)	Lowest Effective Tax	Highest Effective Tax
1	$0	$102,316	$0	10%	10%	10%
2	$102,316	$204,632	$10,232	18.13%	10%	14%
3	$204,632	$306,948	$28,751	32.97%	14%	20%
4	$306,948	$409,264	$62,515	45.12%	20%	27%
5	$409,264	$511,580	$108,660	55.07%	27%	32%
6	$511,580	$613,896	$165,036	63.21%	32%	37%
7	$613,896	No Limit	$229,699	37%	37%	37%

 The 2022 TCJA Tax rates for Married Filing Jointly or Qualifying Widow (Widower) are: 

Bracket	Lower income	Upper Income	Fixed Tax	Marginal Tax Rate  (on amount above lowest income in bracket)	Lowest Effective Tax	Highest Effective Tax
1	$0	$20,550	$0	10%	10%	10.0%
2	$20,550	$83,550	$2,055	12%	10%	11.5%
3	$83,550	$178,150	$9,615	22%	11.5%	17.1%
4	$178,150	$340,100	$2,055	24%	17.1%	20.4%
5	$340,100	$431,900	$9,615	32%	20.4%	22.8%
6	$431,900	$647,850	$2,055	35%	22.8%	26.9%
7	$647,850	No Limit	$9,615	37%	26.9%	35.7%*

*The highest effective tax rate in the highest tax bracket is not reached until the income is infinite. This is the effective tax rate at an income of $5,000,000.

 As can be seen for the TCJA tax brackets, the brackets are not equal AND the effective tax rates are confused with the marginal tax rates. This second error is like confusing speed and acceleration, since both are first and second derivatives.  The combination of these two errors results in a tax code that does not transition between the lowest rate and the highest rate according to the distribution of income. As can be seen in the figure below, this means  the incomes below ~$300,000 are currently paying effective tax rates that should be charged only at higher incomes. The basic errors were made beginning with the “Reagan” Tax Cuts of 1981 and have resulted in an over taxation of the poor and middle class and an under taxation of the rich for over 40 years. If the intent were to transition from the lowest tax rate to a maximum tax rate according to the distribution of income, a math professor would give these tax codes a failing grade.

 

Tax Brackets II

 

Tax Man

Should five percent appear too small

Be thankful I don't take it all

'Cause I'm the taxman

Yeah, I'm the taxman

But  the Taxman should also be the Math Man

I was just preparing to file my taxes when I realized that the Tax Brackets violate the basic Laws of Math. Mattel’s old Talking Barbie doll might be correct, “Math is Hard,” (personally I don’t think it is), but Math also does NOT permit lies. That is why there are Laws and Proofs in Math. The current Tax Brackets are NOT equal. The tax is on the income of individuals, not on individuals. The distribution of income is not equal among individuals. The distribution of income is nonlinear. That is an acknowledgement of fact, not a judgement. According to the laws of calculus, any nonlinear curve can be approximated by a series of straight-line segments, as long as each line segment is of an equal interval. And IMHO, that is where the current Tax Brackets fail.

Without addressing what the marginal tax rate should be in each bracket, a basic principle should be that each bracket be of the same size. And by inspection it is not. Without arguing what the lowest income in the top bracket should be, let’s just accept that amount. The equal interval, size of the tax bracket, should be that income in the highest bracket divided by the number of brackets before that income. In the current tax code that upper income varies by tax filing status (Single, Married filing jointly, etc.) but it is a specified amount. To calculate the size of the brackets correctly according to Math is simple. Divide the lower income in the highest bracket by 6 (the number of brackets before that highest bracket.)

Because the brackets are not equal, the median ( and the median should be used, NOT the mean)  taxpayer is paying a higher tax than would be expected. And the upper income bracket is paying a lower tax than would be expected.  I suspect that the Debt Limit and the federal budget would be less likely to be an issue if the Tax Brackets properly acknowledged basic Math.

Random II

 

Fine and Dandy

Honey, I'm so keen on you
I could come to lean on you
On a random bay, give you your way
Do what you say

And not only a bay, but life is random

"Rule #1 is young men die. And Rule #2 is doctors can't change Rule #1.  So goes one of my favorite lines  from the TV sitcom M.A.S.H.  And while it was dealing with the inability of doctors to prevent death in the Korean War, it sums up the random nature of life and how humans can’t change that randomness.  We can bemoan randomness. We can try to deal with the impacts caused by randomness. But we can’t change the fact that it is random.

And the fact that life is random, and that a human life is short, is why there is free will.  The fact that we are free to choose is why it is random.  The fact that a human life is short and will end is why those choices matter.  We can pretend that solutions are deterministic and repeatable, but that does not make them less random, it only means we are picking the optimal random solution.  In my profession of Traffic Forecasting, if we are not using a maximum entropy/maximum likelihood/most probable process to pick the most probable solution and are instead picking a random solution from a list, we often use a pseudo random number generator to  make it repeatable.  But the fact that appears to be deterministic, does not make it deterministic. In fact, it proves that it is random.

Global Trade

 

Money, Money

A mark, a yen, a buck or a pound
A buck or a yen
A buck or a pound.
Is all that makes the world go around
That clinking, clanking sound
Can make the world go 'round

Or maybe a Bancor?

The United States has a fiat currency.  The role of the US Treasury is to ensure that its fiat currency accommodates all economic transactions in the United States..  The US economy is just over $23 trillion.  To accommodate these transactions then the total US Dollar, USD in circulation, should be  $23 trillion.  But these are not the only economic transactions that use the USD.  Global Trade is $32 trillion and 50% of that amount is invoiced in USD.  Thus, arguably, the dollars in circulation should be equal to $23 trillion PLUS 50% of $32 trillion, or $39 trillion.  If the USD in Global Trade remained in Global Trade, this may not be a problem.  But the persistent inflation since the US Dollars in international trading were taken off the gold standard by the 1971 Nixon Shock, might be due to international USD competing with domestic USD for the same goods. Global Trade has increased by 8% a year since 1975, the founding of the World Trade Organization. Because the US Dollars in circulation do not consider this increase in demand, I would suggest this growth also might explain  the persistent increase in inflation since 1971. The Year Over Year inflation might have declined since the rates in the 1970s, but because the economic transactions requiring the USD have not been properly considered, is IMHO why we have currency inflation greater than 0%.

Another major currency used in International Trade is the Euro.  Arguably the recent economic crises in Greece and Italy could have been  resolved more quickly, if there was an International Currency that was NOT the Euro, and there were still national currencies.  IOW, Keynes was correct all along.  Bring back the Drachma, and Lira and make the Bancor, not the USD or the Euro, the international trading currency. 

Politics

 

Politician

I'm a political man and I practice what I preach.
I'm a political man and I practice what I preach.
So don't deny me baby, not while you're in my reach

Do Politics have to be so Nasty?

Political Parties, factions, were not desired and thus not anticipated by the US Constitution. This is why one of the earliest crisis of the nation was the Presidential Election of 1800.  The problem is that in a single representative per district election system, which is a difference between the US and Europe,  two political parties are inevitable according to, Duverger’s Law.  The problem is that according to Game Theory, a system with only two players will devolve into rewarding nasty behavior.  It is only when there are at least three players that Nice behavior is an optimal behavior.         
https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html

So what is the solution?  IMHO, Sarah Palin’s recent election loss in Alaska has shown the way, Ranked Choice Voting. https://dbeagan.blogspot.com/2022/09/ranked-choice-voting.html .There have to be at least three candidates for Ranked Choice Voting to be meaningful.  So how do you get at least three candidates in a two party system.  I would propose that each ballot in an election includes the party primary winner and the party endorsed candidate.  Often they would not be the same, in which case even when there are only two parties there may be as many as four candidates.

There are already effectively three  parties in the United States: Democrat, Republican AND Independent/Undeclared.  Having only candidates from two parties when there are effectively three parties is IMHO the problem why the US is in its current state.  When independent/third parties candidates run, they often decide the result of the election and it is exactly opposite of what the independents intended.  If there are two candidates from each party, then independents can vote for someone, instead of against someone.

Teachers

 

Teacher’s Pet

Teacher's pet (pa dumb pa dumb pa dum)
I want to be teacher's pet (pa dumb pa dum)
I want to be huddled and cuddled as close to you as I can get

There are good teachers and bad teachers, but you can learn from both.

As background, I graduated from a parochial high school. In Gym Class (or PE, whatever they call it these days), which I had in the middle of the school day, I had lots of textbooks and notebooks that would not fit easily into my Gym Locker.  To cope with this, I always put my textbooks and notebooks just outside the Gym on a public shelf, not in my locker.  One day in my senior year, after Gym Class, my books were gone from that shelf.  My reaction was “so it goes” and I went to my next class.  While in that class, I received a summons to the Principal’s office, which in my “goodie two-shoes” life was a rare event.  The Principal wanted to say that he had taken my books.  The Principal asked wasn’t I afraid that someone was going to steal them. My reply was innocent, but in hindsight the best answer. ”Gee, Brother, no one ever stole them until you did.”  Project much?  In my experience, those who complain the most about a crime are most probably guilty of that crime. 

A postscript.  In two years that Principal went on to become the eastern provincial of his order, the Brothers of the Holy Cross, CSC.  One of his first official acts was to remove the order from my High School. I don’t think that it was for financial reasons, because it was immediately taken over by the Christian Brothers who have operated it successfully for more than more than 50 years.  BTW, the CSC order also operates Notre Dame.  Guess who I always root against in College Football? 

But one bad apple does not spoil the orchard.  That order also included my high school chemistry teacher.  When a neighboring public high school sent a delegation to attend our classes, after the school day, that Brother was moderating a discussion attended by those students and my classmates.  A comment was made by one of my classmates that our high school had the superior education because it was taught by a religious order.  That Brother said that it was not true.  Our school was operated because in the past, Catholics had been discriminated against in public schools.  Because of its size and resources, our school was not able to offer advanced classes (which are now called AP classes).  He said that in an ideal world, there would be no need for parochial high schools and no one would be discriminated against. 

Good or bad, you can learn from either.