Not to put too fine a point on it, since overall your calculations seem fair and your conclusions reasonable: but at $18200 with $10300 in deductions and exemptions the person's AGI would be only $7900 and hence all of their taxable income falls into the 10% marginal tax bracket. Of course this neglects payroll taxes (you did as well) but also ignores the EITC so suppose these roughly cancel. This results in the tax burden being $790 rather than your calculated $2730. That $2000 is a huge deal to a minimum-wage earner. Your back of the envelope calculation in this specific area was off by 450%.