American colleges are spending a declining share of their budgets on instruction and more on administration and recreational facilities for students, according to a study of college costs released Friday.

The report, based on government data, documents a growing stratification of wealth across America’s system of higher education.

At the top of the pyramid are private colleges and universities, which educate a small portion of the nation’s students, while public universities and community colleges, where tuitions are rising most rapidly, serve greater numbers and have fewer resources.

The study of revenues and spending trends of American institutions of higher education from 1998 through 2008 traces how the patterns at elite private institutions like Harvard and Amherst differed from sprawling public universities like Ohio State and community colleges like Alabama Southern.