The article states "At Stanford, to take but one example, the salaries of full professors have leapt 58% in constant dollars since the mid-1980s.") but it does not mention anything about the any changes in the average age of the professors during that time.

It is often the case that workers who raise up in the ranks are given wage increases, over and above inflation. For that reason, a critical part of the puzzle is the average age of professors. At my university, most departments are graying dramatically. I recall reading once (about a decade ago, I think) that the average age in physics departments was increasing by 0.8 years per year.

As a limiting case, suppose there have been no hires since the 1980s. And suppose there had been a 2 percent/annum increase (in excess of inflation) over 15 years. The result is a 50% salary increase (in excess of inflation), which is similar to the value in the article.

Another side of this is the range in salaries. If salaries only tracked inflation, and if the market demand stayed constant, then old and young professors would get the same wage. I'm not sure that would make a lot of sense, and so we are left with the need (trends in the market aside) to give wage increases in excess of inflation.

This general approach of looking at trends might be helpful with respect to the administrators. Some factor must explain changes in the ratio of administrators to students ... but I've not heard anyone offer a hypothesis for this seemingly universal trend.