beac0n's blog

The topic of “who contributes how much” in relationships, where partners live together often times leads to heated arguments.

I came up with a formular, that tries to calculate the most fair amount, that each partner has to contribute to a joint banking account, which is used to pay all common expenses.

I will use “partner A” and “partner B” to describe each partner in the relationshship.

The formular needs the following variables:

income_a: Current income of partner A after taxes
income_b: Current income of partner B after taxes
income_a_single: Income of partner A after taxes, if partner A would be single and had no kids
income_b_single: Income of partner B after taxes, if partner B would be single and had no kids
amount: Amount of money that the couple needs for their common expenses per month
f = max(income_a_single, income_b_single) / min(income_a_single, income_b_single): fairness factor - how much more the “higher earner” partner earns, compared to the other partner

Up until this point, everything can be calculated easily, because it is well known how much each partner earns and also what they would earn if they where single.

To calculate now how much each partner has to transfer to the joint account, we have to use that fairness factor, that we calculated earlier:

income_a * p_a + income_b * p_b = amount, where
- p_a: how much percent partner A pays of amount
- p_b: how much percent partner B pays of amount
f = (income_a * (1 - p_a)) / (income_b * (1 - p_b)), where
- income_a * (1 - p_a): the amount of money that partner A has, after they transfered their share to the joint account
- income_b * (1 - p_b): the amount of money that partner B has, after they transfered their share to the joint account

To calculate p_a and p_b, we have to solve the equations for p_a and p_b:

p_a = (amount*f - income_b*f + income_a) / (income_a * (f+1))
p_b = (amount + income_b*f - income_a) / (income_b * (f+1))

Which leads us to the final amounts for partners A and B: amount = amount_a + amount_b, where

amount_a = income_a * p_a: amount that partner A has to transfer to the joint account
amount_b = income_b * p_b: amount that partner B has to transfer to the joint account

The idea is, that the ratio between the incomes of partner A and B that they earn if they would be single, is still the same after they have transferred their shares to the bank accounts.

Example:

Partner A earns 2000€ a month if they would be single, partner B earns 1000€ a month if they would be single: f = 2.

They both have common expenses of 1000€ a month.

Partner A and B are now married and partner A now earns 2500€ due to tax reasons and other benefits that they have because of their marriage and partner B now earns 850€, because they reduced the workload to take care of kids or for other reasons that contribute to the partnership (e.g. had to take a less well paid job, because both moved to further partner As carreer).

After calculation, this means that partner B would have to contribute 66.66€ and partner A would have contribute 933.33€.

Partner B would have left: 850 - 66.66 = 783.34€ and
Partner A would have left: 2500 - 933.33 = 1566.67€.

The ration between the money that both partners have left is still 2: 783.34 * 2 = 1566.68€.

Of course the values can change dramatically, depending on personal circumstances.

The general idea however is, that both partners contribute their fair share, given their current income, compared to what they could earn, if both would focus only on their carreer given their respective fields. This formular tries to factor in the care work that is often done by one partner, while the other one contributes more financially to the partnership.