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We model the quantities appearing in Internal Revenue Service (IRS) taxguidance for calculating the health insurance premium tax credit created by thePatient Protection and Affordable Care Act, also called Obamacare. We ask thequestion of whether there is a procedure, computable by hand, which cancalculate the appropriate premium tax credit for any household withself-employment income. We give an example showing that IRS tax guidance, whichhas had self-employed taxpayers use an iterative fixed point procedure tocalculate their premium tax credits since 2014, can lead to a divergentsequence of iterates. As a consequence, IRS guidance does not calculateappropriate premium tax credits for tax returns in certain income intervals,adversely affecting eligible beneficiaries. A bisection procedure forcalculating premium tax credits is proposed. We prove that this procedurecalculates appropriate premium tax credits for a model of simple tax returns;and apparently, this procedure has already been used to prepare accepted taxreturns. We outline the problem of finding a procedure which calculatesappropriate premium tax credits for models of general tax returns. While thebisection procedure will work with the tax code in its current configuration,it could fail, in states which have not expanded Medicaid, if a certaindeduction were to revert to an earlier form. Future policy objectives mightalso lead to further problems.

The Affordable Care Act and the IRS Iterative Fixed Point Procedure