Ari: The M.B.A. and M.P.A. are considered terminal degrees (highest degree awarded) and advanced professional degrees in the field of study. Yes, there are Ph.D.s in business. However, the M.B.A. is accepted as a terminal degree in that field, at least in the United States. Individuals typically don’t put M.A. or M.S. behind their names since those aren’t terminal degrees. For example, in a college English department, a professor may have the M.F.A. (Master of Fine Arts) for creative writing, which would be the equivalent of another professor who teaches literature or linguistics with a Ph.D.
I would follow the protocol of your professional field when using the letters behind your name. In your case, using the M.P.A. behind your name is acceptable since the M.P.A. is considered an advanced professional degree for your field. Plus, some positions you apply for may require it.