Earlier quoted context omitted.
Monotonic is what we have, and it allows cliffs. Suppose, e.g., that you can get $5k/yr in benefits if you make less than $10k/yr in other revenue and $0 otherwise. Unless you have a viable strategy for pushing past $15k/yr it's a strong financial disencentive against actually working, and even then your incremental ROI isn't very good past that cliff (if it takes an extra hundred hours to push to $15.1k/yr, then com…
This doesn't sound monotonic. This sounds like a mapping from pre-benefit income to post-benefit income which sends just under $10k/yr to just under $15k/yr, but sends just over $10k/yr to just over $10k/yr. So it sends a larger input to a smaller output.
I'll go further and say what we probably want is for the derivative of net income as a function of earned income to be monotonic increasing but max out less than 1. So that there aren't ranges of income where you are receiving very little per dollar earned and then after some point start receiving more per dollar.
But solving benefit cliffs really just means having earned=>net income strictly increasing with the marginal rate reasonable, say at least 30 cents more net income per earned income. Under that constraint, you could have ranged where net income grows slower until you hit some higher dollar amount of earnings, but imo that should also not be desirable.