I am currently a Ph.D. student with a Master's degree. Throughout my time in grad school, I have been an adjunct at a local university. Recently, this university has started a Master's program in my field. However, the department is quite small and those faculty who are able/interested in teaching these classes is even smaller thus, I have been asked if I would like to teach one of the graduate classes for this new program.
My question is whether or not it would be appropriate for me to ask for a pay increase to teach this course. Currently the adjunct pay is determined by a per unit rate depending on level of education (in my case Master's). What I am unsure about is if this rate should change, or if it is common in other institutions for pay to increase when teaching grad level courses.