The L-39 in the video is powered by an Ivchenko AI-25, from the footage we see that the engine idles at 60% N1, and the taxi power setting is 70% N1. (The other lower-reading needle is the N2.) The same engine powers the Yak-40.
Compared to modern jet engines on airliners, those values are very high.
If 70% N1 is used to taxi, then I think the AI-25's power curve is exponential, and it starts off late. So in a sense there are only two thrust settings, i.e., narrow throttle range, and hard to fine tune.
The AI-25 is a medium bypass turbofan.
I've come across some power curves for jet engines, some are almost linear, some are exponential, and idle RPM varies.
So, what factors influence the idle RPM, and the shape of the power curve?