The presence of deductions has a nasty side effects, both the average and marginal tax rates becomes dependent on the deductions one can claim for a given level of income. The new tax equation is easily derived in function of the previous equation
* D, a vector of deductions
* E, a vector of exemptions
* T0, the tax equation defined before
The rates at a given income are now dependent on the deductions and exemptions. In other words, two taxpayers with the same income and filling status can be taxed wildly differently, based on which deductions and exemptions apply to them. Obviously also, people are aware of this and may adapt their lifestyle to maximize deductions, at least when possible. This is in some sense, why deductions are introduced in Congress, but sometimes with unintended side effects.
An obvious side effect is to introduce societal tensions between people able to claim specific deductions and people unable to claim them. A second side effect is the complexity of the rules needed to administer the different deductions, impacting both the taxpayer and the IRS.
An extreme example compares the federal tax and corresponding average tax rate for two couples filling jointly in the figures below. The first couple has no kid and don't itemize deductions, the second couple has three kids and itemize major deductions that scale as a percentage of the income: 7% state tax, 25% of mortgage interest and 7.5% of medical expenses (their total medical expenses is 15% of income, the first 7.5% cannot be deducted).
Because in this model the deductions are proportional to the income, the two curves diverge, asymptotically the ratio between the marginal rates is 1 - the total percentage of deductions, or about 0.6 in the example. It is a matter of discussion if such a difference makes sense, i.e. is it equitable to favor specific behaviors though differences in taxation rates?
And the difference is huge, the next figure shows the ratio between the tax paid by the couple with three kids and using aggressive deductions and the tax paid by the couple with no kid and using the standard deduction. The ratio never even reaches 50% for the range of income considered here, with the asymptote at 60% as explained before.
Deductions can so much reduce the tax paid that two different mechanisms are in place to avoid their abusive use: phaseouts and the Alternate Minimum Tax (AMT). Both of these will be discussed later on, after an article on tax credit.