so says Professor Perry:
Bottom Line: Private schools can educate students at a lower cost, with more teachers per 1000 students, than the public schools. Reason: Private schools must have significantly fewer non-instructional administrative employees, and therefore significantly lower administrative expenses than their public counterparts.
Update: Professor Perry just keeps knocking it out of the park. He has another post documenting the huge growth in administrative overhead. It far exceeds the growth in students.