J. Paul Robinson, chairman of the Purdue University faculty senate, walks the halls of a 10-story tower, pointing out a row of offices for administrators. “I have no idea what these people do,” says the biomedical engineering professor. Purdue has a $313,000-a-year acting provost and six vice and associate vice provosts, including a $198,000-a-year chief diversity officer. Among its 16 deans and 11 vice presidents are a $253,000 marketing officer and a $433,000 business school chief. The average full professor at the public university in West Lafayette, Ind., makes $125,000.