Income Taxes II

 

Georgia Tech Fight Song 

I'm a Ramblin' Wreck from Georgia Tech
And a hell of an engineer 

What does an engineer think of the income tax code? 

Engineers, such as me, think Talking Barbie is correct. Math is hard.  Engineers try to come up with “Rules of Thumb” to use that are close to being correct.  Mathematicians would say is not possible to state Pi exactly because it is an irrational number. Engineers might say “Let’s just get close enough”.  If engineers said that Pi was 3, then this would result in 4.5% error in computations, which is not close enough.  If engineers said that Pi was 22/7, then the error in computations would be only 0.4%, which is probably close enough.  Similarly, non-linear equations, especially non-linear equations of an exponential since the exponential itself is another irrational number, are approximated by engineers as a series of linear equations, also known as straight lines. 

The mean income by quintile (i.e. 20% ranges) is reported annually by the US Census, which also reports the mean income of the top 5 percent. Assuming that the mean income of a quintile is the income of the midpoint of that quintile, or in plain English, if between 20% and 40% of the incomes had a mean income of $12,196 in 2019 dollars, the income at 30%, the midpoint of that quintile, is assumed to be $12,196.  With this assumption, the reported incomes by quintile can be shown to follow an exponential association with a fit of 95.3%.  The transient income, the only coefficient needed for this equation, is $53,450.26 .  This exponential association can be approximated by a series of 6 simple linear equations, with a correlation of 99.88%, as shown in the following figure.

An equitable distribution of income taxes should follow this same distribution of income.  The taxes should thus be 

Taxes = Income * Maximum Tax * Distribution of income

If the distribution of income is approximated by six linear equations, which are the equivalent to tax brackets, and the transient income which is defined by the income distribution is $53,450, then if the median rate is 20%, the Maximum tax rate should be twice that amount, or 40%.  (In a normal statistical distribution, the maximum is approximately twice the mean.)  The effective tax rate is the actual taxes due divided by the income. 

The 2020 ideal tax brackets which reflect the distribution of income are: 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	1	$53,450	14.7%	$-	14.7%	14.7%
2	$53,451	$106,901	30.7%	$7,865	14.7%	22.7%
3	$106,902	$160,351	36.6%	$40,682	22.7%	27.3%
4	$160,352	$213,802	38.7%	$99,335	27.3%	30.2%
5	$213,802	$267,251	39.5%	$182,164	30.2%	32.1%
6	$267,252	∞	40.0%	$287,827	32.1%	40.0%

The actual 2020 rates from the IRS according to those established in the Jobs and Tax Cut Act,  JTCA, are 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	1	$9,875	10.0%		10%	10%
2	$9,875	$40,125	12.0%	$988	10%	12%
3	$40,125	$85,525	22.0%	$4,618	12%	17%
4	$85,525	$163,300	24.0%	$14,606	17%	20%
5	$163,300	$207,350	32.0%	$33,272	20%	23%
6	$207,350	$311,025	35.0%	$47,368	23%	27%
7	$311,025	∞	37.0%	$83,654	27%	37%

The Marginal Tax Rates on income above the lower amount are comparable between the ideal and actual tax brackets.  The major difference between the two tables is the size of the tax brackets. They should be equal in a tax code based on income distribution.  There would be six tax brackets. The range of the tax brackets would be equal to the transient income as established by the distribution of income.  The actual ranges of income covered by the TCJA tax brackets are not equal and are much lower in the lower brackets.  Consequently the fixed amount (i.e. the taxes on the lower income in each bracket)  is lower for the upper brackets.  This results in effective rates that are far less than would be suggested by the income distribution. The upper tax brackets consequently have been paying effective tax rates that are much lower than would be suggested by the distribution of income. 

These lower than ideal effective tax rates have been in place since the Economic Recovery Tax Act of 1981.  If this was intentional, talk about a long con.  The inequality caused by that, and subsequent tax acts, may have been responsible for the growing wealth gap in the United States.  An income tax code should be based on the distribution of income.  In 1980, before that Tax Act was enacted, the transient income, T, the measure of the distribution of incomes, was only $39,622 in 2019 US Dollars .  A tax code which reflects the distribution of incomes at any T is shown below.  

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	0	$T	14.7%		14.7%	14.7%
2	$T	$2T	30.7%	14.7%*T	14.7%	22.7%
3	$2T	$3T	36.6%	45.4%*T	22.7%	27.3%
4	$3T	$4T	38.7%	72.0%*T	27.3%	30.2%
5	$4T	$5T	39.5%	120.7%*T	30.2%	32.1%
6	$5T	∞	40.0%	160.3%*T	32.1%	40.0%

Adoption of new marginal tax rates may be a "Bridge Too Far" politically.  However adjustment of the ranges of income within each tax bracket might be undertaken which would more closely reflect the distribution of income.  The lowest tax bracket may not be necessary but it is retained here. The changes in the range of income in brackets effects the fixed amount, the amount due on income in the lower brackets, as well as beginning the highest tax rate at a lower income.  This lowering of the lower bound of income in the highest bracket actually has the effect of raising taxes for the current lowest income in the highest bracket because it increases the fixed amount due from taxes on income in lower brackets.  The proposed changes are shown below in red bold font. 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper
1	1	$9,875	10.0%		10%	10%
2	$9,875	$53,450	12.0%	$988	10%	14%
3	$53,451	$106,901	22.0%	$7,402	14%	18%
4	$106,902	$160,351	24.0%	$19,161	18%	20%
5	$160,352	$213,802	32.0%	$31,989	20%	23%
6	$213,803	$267,251	35.0%	$49,093	23%	25%
7	$267,252	∞	37.0%	$67,800	25%	37%

The change in the tax bracket ranges, would lower the tax rate for the all incomes.  It would also lower the total amount of revenue raised by the income tax.  If the tax code is changed, it is suggested that marginal rates that more closely reflect the distribution of income should also be enacted.  As shown in the figure below, this would lower significantly the income tax rate for all those below approximately $140,000 while raising the tax rates for those with incomes above this amount.  However, these tax rates would more closely match the distribution of incomes.

The