State agencies want to spend more than twice the approximately $84 million increase Gov. Norm Bangerter expects an improving economy to generate in taxes next year.

But department heads seem to understand they will not get everything they want, officials said Wednesday. Bangerter, meanwhile, has not ruled out asking lawmakers for a tax cut in light of an apparently rebounding state economy.Bangerter finished several days of listening to requests from state agencies Wednesday. His face showed little emotion as his listened. Only occasionally did he ask a question or make eye contact with the presenter long enough to give an understanding nod.

He will spend the next several days hammering out his recommended budget behind closed doors with his staff before presenting a final version to lawmakers. After receiving Bangerter's recommendations, the Legislature will prepare the final budget during its regular session early in 1989.

State agencies have asked for a combined total increase exceeding $179 million to spend during fiscal 1990, according to figures compiled by Dale Hatch, director of planning and budget.

The largest request for more money came from the state Office of Education, which presented a wish list totaling $79 million more than the current fiscal year.

However, unlike last year when both sides exchanged harsh words over the need for more money, education officials this year arranged their requests according to priorities and said they realize they will not receive everything they asked for.

"We're not asking for a set amount," said James Moss, state superintendent of public instruction. "We're asking for them to consider our requests based on the amount of new revenue that is available.

"We can live with whatever is available. Teachers have been doing that for years. The problem is every time you fail to fund education, the potential for quality education suffers."

The top priorities are to fix shortfalls in retirement and Social Security funds, Moss said. The wish list also includes pay raises totaling 5 percent.

Bangerter, who was narrowly elected to a second term last month despite criticisms over a large tax increase in 1986, said the requests from state departments add up to much more money than is available. He also is expecting a surplus of about $14 million by the end of the current fiscal year.

"We have more wiggle-room in our budget this year than last year," he said. "But not as much as everyone would like."

The governor said he is not ready to decide whether to ask for a tax cut. Voters last month rejected three ballot initiatives that would have drastically lowered taxes, but the tax-protest movement that spurred the initiatives got the attention of state elected officials.

Tax protesters supported independent gubernatorial candidate Merrill Cook, who earned 21 percent of the vote and may have affected the election's final outcome.

"We're well aware that people are watching the tax situation," Bangerter said.

Bangerter said the rigors of campaigning put him behind schedule this year in preparing his budget recommendations. He is required by law to submit a 1990 fiscal budget to the legislative fiscal analyst one month before his annual speech to the Legislature - a speech that must be given within the first three days of the legislative session that begins Jan. 9.

The governor answered cautiously when asked about the possibility his recommendations will include pay raises for state employees. "I think there should be something to enhance their benefits package," he said.

Hatch said the state would have to pay $12 million for each percentage increase in the salaries of state employees. All but $2.5 million of that would go to employees in the education system.

The state's health insurance premiums are expected to rise dramatically next year. Hatch said it would cost the state the equivalent of a 3 percent raise, or $36 million, just to keep up with the increase. The state pays 90 percent of its employees' premiums.

Other requests for budget increases above current levels include: higher education, $28 million; social services, $17 million; natural resources, $17 million; health, $12 million; corrections, $10 million; economic development, $7 million; and public safety, $2 million.