What factors determine the power curve of a jet engine? From YouTube

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.

Update:

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?
Not a direct answer, but one thing to keep in mind is that thrust has very non-linear dependency on RPM. 70% N1 may mean 20-30% thrust. (And that's static thrust; in flight the difference may be even greater).

I don't have exact figures for AI-25, but for a similar engine I remember the gradient near 100% was around 5 (5% thrust for each 1% N1).

Actually, I have some data for Williams FJ33, which is comparable.

On the ground, it idles at 25% N1, which is only 3% of thrust. For 50% N1, you still have less than 20% of thrust. 60% N1 -> ~28%, and for 98% N1 you have over 100% of static thrust.

By the way, AI-25 on L-39 is 'overrated' compared to Yak-40 and its N1 goes to 107%, if I remember correctly. So it's all not that bad.