I've been trying to find the function of the s-shaped poverty trap curve for a while now. Unfortunately while I know what it looks like I have no idea what the function is. There are very strict requirements for the curve: it needs to intersect the 45 degree line and the distances between each intersection should be monotonically increasing. The intuition is that intersections correspond to monotonically increasing thresholds for poverty traps.
I'm assuming that there's an exponential in there somewhere. It's been 10 years since I graphed anything so please give me a hand math wizards. I have a picture of an example below
