The Farm Household Allowance used to have a “gradient” payment: If you earn a little more private income, you get paid a little less welfare. The Allowance gives farmers up to 1460 days of payment; for each day of pay, they lose a day on the “clock”. Once their 1460 days run out, they cannot receive further payment. Given that a farmer might be eligible for, say, half the maximum rate of pay, some eligible customers face a dilemma—get paid half the max rate now, or save that day of pay because they might get a max-rate payment in the future. This dilemma shouldn’t be faced by customers who are under financial distress.

To avoid this issue, we changed to an “all-or-nothing” payment: You’re either at the max rate or you get nothing. Unfortunately, this new payment creates another issue: If someone is $1 below the income threshold, they get the maximum payment, which is several hundred dollars; if they earn $2 more, they lose all of it. This is a strong disincentive to earn more money when you’re right below the threshold. Customers should never be worse off from earning more private income.

After identifying these issues, I figured out how our desired properties for our payment could be represented mathematically. These representations let us evaluate whether the issues are avoided by any given payment proposal.

To ensure it’s always in the interests of eligible customers to apply, the discounted sum of payments (assuming a positive interest rate) must always be maximized when the customer applies as soon as possible.

To ensure more private income is always better, the following equality must hold:

My proposed alternative avoids both issues. I proposed we have a gradient payment and if someone is paid at, say, 17 percent of the max rate, they lose 0.17 days off the clock per day (rather than a full day).

There’s a lot of payment functions that satisfy these properties (e.g. “Pay everyone zero welfare”, or “Pay everyone a million dollars”). In other words, these properties are necessary but not sufficient. You want more desirable properties to justify your system. Ideally, you want your properties to cut down your options to only one possibility.