The tax is dependent on income, but what exactly is the income used in
the tax equation?

Well, this is where the difficulties begin. Tax laws come from Congress
that cannot resist its urge at pleasing specific parts of the
population by introducing tweaks, normally in the form of deductions
linked to specific conditions like marriage, house ownership, children,
.... The base principle becomes the tax law that is then formalized in
specific rules by the IRS, i.e. what is the definition of a kid.

Because the world is not as regular as can be expressed in a law, the
IRS rules are complex, full of details that apply probably only to a
very small percentage of cases but still must be detailed in the
instructions booklets written by the IRS.

The income used in the tax equation is known as the adjusted gross
income, it is essentially calculated as follows for your workpay:

* start with your nominal salary

* remove a number of special items: social security, 401k
contributions, ... and you get your taxable income

* remove the exemptions, these are usually amounts that are
not directly related to any real expenses

* remove deductions, these are usually amounts that
correspond to specific expenses that are considered useful for the
society, at least as seen by Congress

* presto, you have your adjusted gross income.

Of course, this is where the pain starts, you as a taxpayer, have to
assemble all the information needed to correctly assess your taxable
income, but also to substantiate your deductions. The IRS estimates are
that filling a 1040 form requires 30.3 hours of which 19 hours are for
record keeping. If you can take 2 hours a day after work, this requires
two
full weeks of work.

The IRS also estimates the average cost at $269, but this probably
assumes your time is free. No surprise this is called a burden.
Of course, the IRS is part of the problem as the rules are at best
complex. Just an example, line 42, Exemptions has special treatment for
persons displaced by Hurricane Katrina. This probably comes from a good
intention, but a first obvious remark is that this is only a very small
part of the population, but it impacts all taxpayers (you have to read
the instructions).

Then there are the exact rules, with no less than 6 small details that
you have to check if you happen to be housing a displaced person, the
first one reads "The person displaced lived in your main home for a
period of at least 60 consecutive days ending in 2006". The definition
appears rigorous, but this is a nice example of how arbitrary the
process can be, note the following:

* main home, what if you have contributed a cottage that is
on the same piece of land as your main home?

* 60 consecutive days, what if the displaced person traveled
for one week, say to New Orleans, is it still consecutive. If you
remember that the displaced person was there in January and February,
can you positively remember that he or she was there for 60 days?

This is not directly a critic of the IRS, but of the whole process of
trying to carve out special cases. Every special case comes with a set
of rules and all these rules will probably raise a number of secondary
questions that may end up as more rules and the cycle never ends. After
a few years of this, you need 30 hours to fill your tax form and
everybody hates filling the form.

But this derails us from the goal, a mathematical treatment of the tax
equation. Mathematically, deductions and exemptions correspond to an
offset. Essentially pushing the tax curves to the right when using the
taxable income for the x axis. This will be further discussed and
illustrated in a next article.

## Wednesday, February 14, 2007

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