LOUISVILLE, Ky. — The average cost of tuition and fees for four years at a public Kentucky university will be more than $39,000 this fall after state regulators approved increases Friday for most institutions.

All but two schools asked for the maximum increase allowed by the Council on Postsecondary Education. The University of Louisville did not raise tuition, and Kentucky State University’s board of trustees has not had a meeting yet to ask for an increase.

Council President Bob King said the board approved the “sticker price” for tuition and mandatory fees. He said students rarely pay that full price because of financial aid and scholarships. But when adding room and board and other fees, he said the net price of attendance for in-state students is about $10,200 per year, or $40,800 for four years.

It is the second time regulators have approved tuition increases since Republican Gov. Matt Bevin cut the budgets for most public colleges and universities. Bevin said the cuts, about $40 million, were necessary to help the state cope with a multibillion-dollar public pension debt. And this year, state economists predict the state will finish the fiscal year with a $113 million shortfall.

Some university presidents warned the budget cuts, compounded with other state reductions since 2008, would require university boards to continue raising tuition. The Bevin administration sharply criticized the increases last year, calling them unnecessary. This year, the only institution not to request an increase was the University of Louisville, whose board of trustees was abolished and replaced by Bevin last year. A state judge ruled Bevin’s order was illegal, but the Republican-controlled legislature passed a law this year to keep Bevin’s board in place.

Western Kentucky University President Gary Ransdell said the budget cuts have been “devastating.” He said the school has lost $18 million in state funding on top of the $18 million trustees have voluntarily removed from the budget as the economy improves and enrollment declines because fewer adults are paying for part-time classes.

Still, Ransdell said the school’s operating budget has continued to grow because “we generate revenue from other sources.” The school’s 3 percent increase approved Friday pushes the price of a full year of tuition and fees to just over $10,000, trailing only the University of Kentucky and the University of Louisville. Ransdell said the 3 percent increase is just enough to cover the university’s cost increases.

“The only way tuition increases will not occur is if state appropriations are significant enough to offset the revenue that they generate,” he said.

Tuition also will be increasing at the two-year schools in the Kentucky Community and Technical College System. The council approved increases of $6 per credit hour, making the cost of a 30-hour course load $4,860.

Regulators also gave final approval to new rules that will make public colleges and universities compete against each other for state funding. The regulations are the final step of implementing a new state funding model lawmakers passed earlier this year.

From now on, 35 percent of state funding for public colleges and universities will be based on the types of degrees awarded. Of that, 5 percent will be determined by the number of science, technology, engineering, math and health degrees; 3 percent based on degrees for low-income students and 3 percent based on degrees for minorities. The model is based on Republican Gov. Matt Bevin and others’ push for more focus on training people for the types of advanced manufacturing jobs state officials are wooing.

The new rules will also reward institutions for enrolling and graduating more students. Ransdell, who led a committee that proposed the rules, said some schools will have an easier time doing that than others.

“It’s going to be a challenge for some institutions whose geographic location maybe isn’t as conducive to growth,” he said. “They are going to be forced to look out of state a bit more to again identify new markets, as we all will be. So this is going to drive behavior on our campuses, and I think that’s a good thing.”