To evaluate whether the tuition fee is reasonable or not , I suggest you to consider the following points :-
a. the qualification of the teacher e.g Grade 8 or DipABRM or FRSM
b. any formal training in music e.g degree/diploma holder in music , graduate from famous music school or APA
c. the teaching experience
d. is this teacher good at teaching kids ?
e. the examination result of the students of this teacher ?
f. does your kid happy in the lesson or like this teacher ?
If you could provide answers to the above questions, a much more appropriate suggestions would be drawn from me and other moms of this forum.
If you feel the teacher is good, $400/hr is valuable because it is very personally feeling. Some of my friends their violin teacher cost them $500/hr door-to-door.