Doing a lower rate with a client in the summer and then raising it in the school year?

I may start working with a Wyzant student (I only use Wyzant in the summer, basically). I struggle to get summer students so basically am willing to get paid at a much lower rate than my school year rate. This family wants me to work with the student for the next year or so, perhaps longer. I'm debating whether to take them on, as I'd love to have the summer work but am not sure if I can fit him in during the school year (and even if I could, I'm not sure I'd be willing to have this extra work at such a lower rate than my other students).

So I was thinking of giving them an honest explanation of what I want: the lower rate in summer, but then once the school year starts I'd have to raise it quite substantially (by like $50-100 more than the summer rate, and even that would be less than what my regular school year students give me). If they'd be willing to do that, then I'd be willing to take them on.

Does this sound fair?

Topic is SAT tutoring (verbal) and College Essays.