By Yereth Rosen

ANCHORAGE, Alaska (Reuters) - Alaska lawmakers on Sunday gave final approval to a bill slashing state oil-production taxes in a change supporters said was needed to boost flagging output from aging fields but which critics say will severely damage the state's finances.

The new system approved by the Republican-dominated legislature does away with a methodology that increases tax rates as oil prices rise, a centerpiece of the aggressive tax legislation championed by former governor Sarah Palin.

Alaska will impose a base rate of 35 percent on oil companies' net profits in the state, replacing a 25 percent base rate that increased by 0.4 percentage points for every $1 above a net wellhead price of $30.

While the old tax system produced billions of dollars in surpluses for the state treasury, it meant Alaska's tax rate topped 50 percent when oil prices were high. Governor Sean Parnell, Palin's successor, said the cut would set the stage for future growth as the state tries to reverse decades of declining oil output.

"We are signaling to the world that Alaska is back, ready to compete, and ready to supply more energy once again," Parnell, who introduced the bill, said in a statement.

Oil production from Alaska's North Slope peaked in 1988 at over 2 million barrels per day, led by the Prudhoe Bay field which averaged 1.6 million bpd that year, according to state Department of Revenue statistics. Production in 2012 averaged 579,400 bpd, with Prudhoe Bay production down to 265,200 bpd.

The tax change was promoted by the three major North Slope oil producers, ConocoPhillips, BP Plc and Exxon Mobil Corp. The companies argued that Alaska's current tax system is punitive and makes the state less attractive than other regions, such as North Dakota and Alberta.

Republicans said the changes would ultimately coax more oil into the aged Trans Alaska Pipeline. But minority Democrats railed against it, with Senator Bill Wielechowski saying it handed over "billions of dollars, with no strings attached."

"It's an epic give-away," he said.

Senator Bert Stedman of Sitka, one of the few Republicans to oppose the tax cut, said if the new system had been in place in 2012, the state would have lost $1.7 billion in revenue from the two major North Slope fields, Prudhoe Bay and Kuparuk.

Stedman said the tax changes granted breaks mostly to the legacy fields, where oil has been flowing for decades and where reductions are unnecessary. "When you make a colossal financial error like this, it's going to be difficult to back up and fix it. And we're going to burn through our savings," he said.

With the tax cut, the state will need to take $861.5 million from savings to balance the budget for fiscal 2014, starting on July 1, said Senator Hollis French, an Anchorage Democrat.

"I'm very concerned that this bill may bankrupt the state," he said, estimating that with credits and exemptions included in the bill, the effective tax rate would be 14 percent.

The legislature on Friday also approved Parnell's bill to authorize $355 million in grants, loans and other financing for a system to bring liquefied natural gas from the North Slope to Fairbanks.

The project would include a small liquefaction plant, a system to truck the LNG to Fairbanks and a distribution system there. Currently, a small amount of LNG is trucked north to Fairbanks from Cook Inlet in southern Alaska. Some regional utilities are considering plans to bring LNG south from the North Slope.

Another bill approved on Saturday by the legislature authorizes funding for an in-state pipeline to bring natural gas from the North Slope to Fairbanks and Anchorage.

Such a project, which would carry up to 500 million cubic feet a day, would cost $7.7 billion, according to the state agency developing plans. So far, no companies have submitted formal plans for such an in-state natural gas pipeline, which critics claim would hinder chances for a large North Slope natural gas export project.

(Editing by Braden Reddall and Edwina Gibbs)