Expecting more students than usual to take them up on an offer of admission, the Graduate School of Arts and Sciences accepted fewer students this year than last.

Graduate School Dean Jon Butler said he expects the school’s yield to rise this year after applications increased 9 percent, largely because a gloomy job market is sending more college graduates back to school. But departments cannot be certain about yield and — at a time when each doctoral student costs the University over $50,000 a year — they are taking steps to avoid straining the budget while maintaining current class size.

“At the most it would be one or two in a number of departments,” Butler said of the reduction in offers. “The problem that every graduate school faces is that yield — except in a few departments — is exceedingly difficult to predict.”

Butler said he anticipates a larger percentage of accepted students to matriculate for several reasons. Butler said he attributes that in part to decisions by some peer institutions to make fewer offers. And the application surge, which indicates greater interest in the Graduate School, Butler said, means more admitted students will likely attend. He declined to say exactly how many fewer offers were made this year than last.

At all major research universities, doctoral students receive tuition, a stipend, and health insurance, costing the institution $50,000 to $70,000 per student per year, Butler said. Preserving the current size of the incoming class therefore lessens the strain on the Graduate School’s budget. But if the yield turns out to be high despite departmental reductions, the class accepted in spring 2010 will have to be smaller to compensate.

“The most problematic impact is on the Graduate School,” Richard Cohn, Director of Graduate Studies for the department of music, wrote in an e-mail. “If every department has higher-than-predicted yields, then there are obviously unbudgeted expenses; and then this inevitably places pressure on future fellowship budgets, or on available funds elsewhere in the university.”

Administrators in the German and English departments they reduced the number of offers they made by one and two, respectively, and acknowledged the potential financial complications of a higher yield.

The trend could play out in different ways across different fields. The humanities and social sciences saw application increases of 10 and 12 percent, respectively. But in the sciences, for example, applications have only risen slightly.

Steven Pincus, director of graduate studies for the history department, said his department accepted fewer applicants this year in order to balance out last year’s unusually large entering class. The economy did make the department more conservative, Pincus said, but he does not think the department’s yield will change. After all, Yale will still be competing with other top universities for the best applicants, he said.

The economics department, however, extended slightly more offers this year than last. Truman Bewley, the department’s director for graduate studies, said he followed his department’s standard method of admitting students: The department calculates the probability that each applicant will choose to attend Yale, and accepts enough of the best candidates to reach the targeted class size. Bewley said he did not consider the possibility of higher yield in making offers, and said the growth in offers made was simply a result of the department’s standard protocol.

“Other schools have cut back and I didn’t know it at the time,” Bewley said.

American studies, political science, psychology, philosophy, and biological and biomedical sciences are among the other departments that said they did not change the number of offers they usually make.