Salary for full-time temporary admin assistant in higher education moving to regular full-time

I have been working as a full-time temporary administrative assistant in a higher education institution. My 12-month contract as a temp ends in December 2018, and my supervisor is seriously considering moving me into a full-time regular (with benefits) position. I am currently paid $15/hr, but my responsibilities have steadily increased during the last 10 months. Would it appropriate to ask for a pay increase, and if so, what would be considered reasonable?

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