I think it's wise to notify students in advance, but I don't think the teacher has a moral responsibility to do so. Of course, if you raise prices, you should expect some of your students to go away. If you suddenly raise prices, don't be surprised if some of your students suddenly vanish. ;-) 

I typically let my active and long-term students know if there will be a price increase in the coming weeks to allow them to book packages at their current rate. It's good for both of us: I'm assured of a sufficiently full schedule in advance and they get to keep the current rate.

I've been surprised when some students didn't take advantage of the heads-up. They were happy to wait and book packages at the new price.

In the past, when my tutoring rates increased quickly and it wasn't practical to constantly send messages to students, I kept my rate the same and individually changed the lesson price for one or two people I really liked working with. 

@Irena

Yeah, my point was that „loyal“ students should be notified. Should have written it clearer. If I took 30 lessons or more with a teacher than I’d expect him to tell me about pricing changes. I would’nt expect that from a new teacher. I just like to plan my budget for language learning classes.

Personally, I never refused to pay higher prices when I was satisfied with the teacher.