In the special case that the tax authority thinks that spillover is zero, then the out partner gets a tax rebate of rH in comparison with the single person. The home partner would not have to pay taxes when H would be less than B (half a day home maintenance work would be less than a day at a minimum wage). In this case the couple has more net income than the single person, and the products of another persons work, though on a pro-person base they would have less. Conversely, if home maintenance is a highly priced good, then there could be a case to levy taxes.
If spillover is a nonzero constant, then there is an income level y where the taxable income of the home partner H +
yo - B will become positive. A person will have to pay taxes ‘just because’ he or she forms a couple with a high income earner. If spillover is nonzero but variable, then the value of
that makes taxable income of the home partner exactly zero follows from H +
yo - B = 0, and appears to be a function of income y:
