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