* C, a vector of Credits
* T1, the tax equation defined before
The most important credit is the earned income tax credit (EITC). The EITC is a very special tax credit, it is refundable, in other words if you end up with a negative tax, the government will effectively send you back some money. Note that this is different from a refund, the EITC is only valid for low income taxpayers and correspond to a work incentive, in a certain range of income, the government chips in some extra money towards your disposable income. The EITC is one of the largest aid programs, as mentioned in "Behavioral Responses to Taxes: Lessons from the EITC and Labor Supply"
In fact, the EITC is the largest cash transfer program for lower-income families at the federal level. An unusual feature of the credit is its explicit goal to use the tax system to encourage and support those who choose to work.
The next figure is extracted from the same document (based on values provided in table 13-14, Green Book, 2004, Joint Committee on Taxation, Ways and Means Committee) and shows the evolution of the EITC. To put things in perspective, the total amount of individual tax liability is about 800 billions in 2003.
As alluded, the EITC increases with an increase in income, mathematically this means negative marginal rates, i.e. your tax decreases (in this case becomes more negative) as your income increases. The exact rates are variable and depend on the phaseout characteristics of the EITC, this will be discussed in the more general article on phaseout effects.